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Tutors Answer Your Questions about logarithm (FREE)
Question 241405: I am trying to solve (2x^2)*(e^2x)-(5xe^2x)=3e^(2x)
this has completely stumped me.
Answer by jsmallt9(591)   (Show Source):
You can put this solution on YOUR website!
One way to solve any complicated equation like this is to get one side equal to zero and factoring it. (This is one the of the techniques you learn when learning to solve quadratic equations.) So we'll start by subtracting  from each side:
Now we'll factor. As usual, always start factoring by factoring out the GCF (unless it is 1). The GCF here is  :
The second factor is a trinomial that will factor, too:
Now, according the the Zero Product Property, this (or any) product can be zero only if one (or more) of the factors is zero. So:
 or  or 
Next we solve each of these. can never be zero, no matter what x is. So there will no solutions from the first equation. The other two equations, however, do have solutions:
 or 
Question 240406: TRUE/FALSE: log (A-B)= log A divided by log B
TRUE/FALSE: log A-log B = log A divided by log B
Answer by Alan3354(6079)  (Show Source):
You can put this solution on YOUR website!TRUE/FALSE: log (A-B)= log A divided by log B
False. For example A = 100, B = 10
Log(A-B) = log(90) =~ 1.9524
log(100)/log(10) = 2
---------------------
TRUE/FALSE: log A-log B = log A divided by log B
False. log(100) - log(10) = 1
log(100)/log(10) = 2
Question 240397: which is greater log base e 10 or log base 10 e? explain
Answer by Alan3354(6079) (Show Source):
You can put this solution on YOUR website!which is greater log base e 10 or log base 10 e? explain
--------
From a calculator:
ln(10) = 2.3026
log(e) = 0.43429 = 1/2.3026
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What's to explain?
Question 241161: expand the expression, log base 4 (4^7 times 3^7)
Answer by JimboP1977(76)  (Show Source):
You can put this solution on YOUR website!log(base4)(4^7*3^7)
log(base4)4^7 + log(base4) 3^7
7 * log(base4) 4 + 7 * log(base4) 3
7 * 1 + 7* log (base4) 3
7 + 7* log (base4) 3
Question 241186: please help me solve this
log (6x+5) - log (3) = log (2) - log (x)
Answer by solver91311(5072)  (Show Source):
Question 241188: ln (3x-4)= 7
Answer by solver91311(5072) (Show Source):
Question 240286: given logx+y/log2 = log x-y/log3 = log64/log 0.125
find the values of x and y
please do reply of d above ques...
Answer by Alan3354(6079) (Show Source):
You can put this solution on YOUR website!logx+y/log2 = log x-y/log3 = log64/log 0.125
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logx+y/log2 = log64/log 0.125
Cross multiply
log(x+y)*log(0.125) = log2*log64
log(x+y) = log2*log64/log(0.125)
log(x+y) =~ -0.60206
x+y = 0.25
-------------------------------
log x-y/log3 = log64/log 0.125
Cross multiply, etc
log(x-y) = log3*log64/log(0.125)
log(x-y) =~
x-y =~ 0.95424
x-y = 1/9
x+y = 1/4
----------- Add
2x = 13/36
x = 13/72
---------
y = 5/72
Question 241166: so im not sure if i need to go another step when they say "write the following expression as a single logarithm"
Equation: 1/4log(x)-slog(y)+7/10log(z)
My anzwer: log(x^4 square root (z^7))/square root (y)
Do i need to go another step?
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(5072) (Show Source):
Answer by Alan3354(6079) (Show Source):
You can put this solution on YOUR website!1/4log(x)-slog(y)+7/10log(z)
My anzwer: log(x^4 square root (z^7))/square root (y)
------------
1/4log(x)-slog(y)+7/10log(z)
= log(x^(1/4)) - log(y^s) + log(z^(7/10))
= 
-----------
I don't see how you got square roots. Is the 's' a square root?
Question 240287: find correct to two decimal places the volume of a cylinder of height = 221.1 cm and base radius 12 cm. ( pie value=3.142)
solve the problem using log.
pls do help me out 2 solve dis problem..
Answer by Alan3354(6079) (Show Source):
You can put this solution on YOUR website! find correct to two decimal places the volume of a cylinder of height = 221.1 cm and base radius 12 cm. ( pie value=3.142)
solve the problem using log.
-------------
V = 100136.25 cc
V = 100.14 liters
----------
I don't see any use for logs.
Question 240762: Solve for b:
logb8=-3
Found 2 solutions by JimboP1977, jsmallt9:
Answer by JimboP1977(76) (Show Source):
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!When the variable is in the argument or the base of a logarithm, you solve for that variable by rewriting the equation in exponential form. This is done by using the fact that  is equivalent to  .
Rewriting your equation in exponential form we get:
Now we have an equation we can solve. There are several ways we could solve this. One would be to raise both sides to the -1/3 power. (You'll see wht when we're done)
which results in:
We have been trying to solve for b and, as you can see, we have been able to do this in one step (raising to the -1/3 power). All that is left is to simpilfy the right side. To do this by hand it helps to factor the exponent:
or
Since 1/3 as an exponent means "cube root of" and the cube root of 8 is 2:
Since -1 as an exponent means "reciprocal of" and the reciprocal of 2 is 1/2:
Question 241116: 2log4-log3+2logx-4=0
Answer by Alan3354(6079) (Show Source):
You can put this solution on YOUR website!2log4-log3+2logx-4=0
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log(16) - log(3) + log(x^2) = 4
log((16x^2)/3) = 4
(16x^2)/3 = 10000
x^2 = 30000/16 = 1875
x =~ 43.301
Note: the negative root is not valid, since log(x) is used.
Question 240106: Could you please help me answer this logarithm? The instructions are: Use properties of logarithms to write the following expressions as a single logarithm with a coefficient of one.
log2(55y)- log2(5x)
Answer by JimboP1977(76) (Show Source):
Question 240400: Evaluate (log base B of B)^2
Answer by JimboP1977(76) (Show Source):
Question 240650: A thermometer that reads 80 degree C is brought into a room that is at 20 degree C. exactly three minutes later, it reads 70 degree C. when will it read 50 degree C?
Answer by JimboP1977(76) (Show Source):
You can put this solution on YOUR website!10 degree drop in three minutes. So 3 and 1/3 drop in 1 minute
30 degrees divided by 3 and 1/3 equals 9 minutes.
Not sure what logs have to do with this unless I am missing something obvious?
Question 240649: 7(1 divided by 7)^7-t=7
Answer by checkley77(7049) (Show Source):
Question 240670: what is the answeat to log8/logx=3
Answer by stanbon(26272) (Show Source):
You can put this solution on YOUR website!what is the answer to log8/logx=3
-------
Cross-multiply to get:
3log(x) = log(8)
log(x^3) = log(8)
x^3 = 8
x = 2
===========
Cheers,
Stan H.
Question 240665: Express in logarithmic form of 64½=8
Found 2 solutions by Theo, jsmallt9:
Answer by Theo(675)  (Show Source):
You can put this solution on YOUR website!The definition of logarithms states:
log(b,x) = y if and only if b^y = x
and:
b^y = x if and only if log(b,x) = y
Since 1/2 = .5, your formula becomes:
64^(.5) = 8
If we let:
64 = b
.5 = y
8 = x
Then, the definition of logarithms applied to your formula states:
64^(.5) = 8 if and only if log(64,8) = .5.
Algebra.com formula generator make it look like this:
 if and only if 
If you put 64^(.5) in your calculator, you will get 8.
If you put log(8)/log(64) in your calculator, you will get .5
log(8)/log(64) is equivalent to  which means log of 8 to the base of 64.
The procedure uses the change of base of logarithm formula of:
This formula states that if you have a logarithm of a number to the base of b, and you want to convert it to a logarithm of the same number to the base of c, you take the logarithm of the number to the base of c and you divide it by the logarithm of the base of b to the base of c.
In your problem, we converted your exponential equation to the logarithmic form to get:
log of 8 to the base of 64 = .5
to prove that was true using the calculator, we had to convert the logarithm to the base of 64 to a logarithm to the base of 10 because the LOG function of the calculator works to the base of 10.
The formula we used was the change of base formula.
We took the logarithm of 8 to the base of 64 and converted it to the logarithm of 8 to the base as shown below:
log of 8 to the base of 64 = log of 8 to the base of 10 divided by the log of 64 to the base of 10.
this became:
 making the result = .5
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!When working with exponential and logarithmic equations, you must learn how to convert from one to the other. The general conversion is
 is equivalent to 
So in
 the "a" is 64, the "b" is 1/2 and the "c" is 8. In the logarithmic form we get:
Question 240559: Solve: 2log(base4)x+log(base4)3=log(base4)x-log(base4)2
Answer by rapaljer(3620) (Show Source):
You can put this solution on YOUR website!
Multiply both sides by 2:
Factor the x:
There are two solutions:
x=0 NOTE: THIS ANSWER MUST BE REJECTED, SINCE log(0) is UNDEFINED!!
6x-1=0
6x=1
x=1/6 This one seems to work!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 240616: P=13500+22ln(t+1), where t is th etime in years from the present. In how many years will there be 18,000 omsects?(round to the nearest tenth of a year).
18,000=13,500+22ln(t+1)
4,500=22ln(t+1)
204.5=ln(t+1)
Answer by rapaljer(3620) (Show Source):
You can put this solution on YOUR website!You are correct so far.
18,000=13,500+22ln(t+1)
4,500=22ln(t+1)
204.5=ln(t+1)
The next step is to "undo" the ln function. You can do this by raising both sides as a power of "e".
Now, subtract 1 from each side:
 , which is approximately 6.5046*10^88 years, which is one HECK of a long time!! Are you sure you copied this problem correctly?? Are all the units given in years???
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 240638: How would i rewrite this as a single logarithm?
3ln(x)+3/4ln(x+1)-ln(2x+3)
Answer by rapaljer(3620) (Show Source):
You can put this solution on YOUR website!First, by laws of logarithms, the coefficients of the ln terms become exponents:
Now, the sum of ln's is a product and the difference becomes a quotient within the ln function, like this:
I have a LOT of resources on my own website on the topic of LOGARITHMS. To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "College Algebra", and look in "Chapter 4"--the entire chapter is LOGARITHMS. This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it MUCH easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.
In addition, I have a video of me teaching this topic in the classroom a few years ago.
To see this FREE video (actually there are TWO two-hour videos!), from my Homepage, look for "Rapalje Videos in Living Color". Select "College Algebra", and look for "Logarithms Part I" and "Logarithms Part II".
If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 240625: how would you graph y=log(subscript 4)x?
Answer by solver91311(5072) (Show Source):
You can put this solution on YOUR website!
I would pick several values for x, calculate the value of y using the base conversion formula, plot the points (x, y), and then draw a smooth curve through the points.
John
Question 240549: how do you solve log base 4 of 16x
Answer by Alan3354(6079) (Show Source):
Question 240520: what is x if: logx(16)=-2
I have x^-2=16
x^-2^-1=16^-1
x^2=1/16
2 squareroot 1/16
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!
All of this...
I have 
 (Rejecting -sqrt(1/16) because x is the base of a logarithm and we don't have logarithms with negative bases.)
... is great. But you should simplify your answer:
Question 240493: Rewrite as a sum and/or difference of multiples of logarithms:
ln((3x^2)/square root 2x+1))....my answer was 2ln(3x) + 1/2ln(2x+1) is this correct?
Found 2 solutions by jsmallt9, jim_thompson5910:
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!You have unbalanced parentheses in your problem so I have to check. Is this the original logarithm?
If yes, keep reading. If not, then please repost your problem with properly balanced parentheses.
Your answer,  , is pretty close. One error is that it should be a difference instead of the sum because of the division in the original log:
This may meet the requirements of the problem. But it is possible to use the property,  , on the first log giving:
I don't know if this last expression would be preferred over  .
Answer by jim_thompson5910(13787) (Show Source):
You can put this solution on YOUR website! Start with the given expression.
 Break up the log using the identity 
 Break up the first log using the identity 
 Convert to rational exponent notation.
 Pull down the exponents using the identity 
So 
Question 240402: solve for X: log (log base e of X)=1
Answer by JimboP1977(76) (Show Source):
Question 240403: if log base e of X =6, then log base e of (eX)=
Answer by JimboP1977(76) (Show Source):
Question 240290: given that log xy=2, logy/x+log 4 = 2, find the values of x and y.
Answer by solver91311(5072) (Show Source):
Question 240279: Express irrational solutions in exact form as a decimal rounded to 3 decimal places.
log2(3x+2)- log4 X=3
Answer by Alan3354(6079) (Show Source):
Question 240207: solve this logarithmic equation & give the exact answer.
log(base)3 (x+6) + log(base)3 (x-6) - log(base)3 x =2
Answer by nerdybill(2446)  (Show Source):
You can put this solution on YOUR website!log(base)3 (x+6) + log(base)3 (x-6) - log(base)3 x =2
log(base)3 (x+6)(x-6) - log(base)3 x =2
log(base)3 [(x+6)(x-6)]/x =2
[(x+6)(x-6)]/x = 3^2
[(x+6)(x-6)]/x = 9
(x+6)(x-6) = 9x
x^2 - 36 = 9x
x^2 - 9x - 36 = 0
(x-12)(x+3) = 0
x = {-3, 12}
.
We can throw out the -3 -- it's an extraneous solution -- leaving us with:
x = 12
Question 240209: solve the exponential equation.
e^2x + e^x -6=0
Answer by nerdybill(2446) (Show Source):
You can put this solution on YOUR website!e^2x + e^x -6=0
.
This is simply a "quadratic equation":
.
Let y = e^x
then
y^2 = (e^x)^2 = (e^x)(e^x) = e^2x
.
So now we can rewrite:
e^2x + e^x -6=0
y^2 + y -6=0
(y+3)(y-2) = 0
y = {-3, 2}
.
Since we said:
y = e^x
ln y = x
.
So,
x = ln 2 (this is your solution)
Question 240208: solve & give the exact answer.
log(base)2 (x+3) - log(base)2 (x+1) =2
Answer by edjones(3295)  (Show Source):
Question 240210: Solve the exponential equation.
e^(3x-5) -1=1282
Answer by edjones(3295) (Show Source):
Question 239898: If LOGaX = 2 and LOGaY = 3, what does LOGaX^3Y equal?
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!If  and  , what does  equal?
Since we know the first two logs, we will find the third one by expressing it in terms of the first two. This is possible because there are properties of logarithms which allow us to manipulate the arguments of logarithms.
First we will use the property  . This allows us to split the log of a product into the sum of the logs of the factors. This will allow us to split apart the  and y:
Next we can use the property  . This allows us to move the exponent on the argument of the log to the front of the log as a coefficient:
Now that has been expressed in terms of  and  we can substitute their values:
Question 239794: find the value of x
1.)logx (3x+10)=2
Found 2 solutions by JimboP1977, vleith:
Answer by JimboP1977(76) (Show Source):
You can put this solution on YOUR website!I got a different answer to vleith. In the question I assumed that log has a base of x? Is this incorrect?
log(base x) (3x+10) = 2 (This means what number power to base x gives 3x+10)
3x+10 = x^2
10 = x^2 - 3x
10= (x-(3/2))^2 - 9/4
(49/4)^(1/2) = x - (3/2)
x = +3.5 + 3/2 OR x = -3.5 + 3/2
x = 5 OR x = -2
Answer by vleith(1977) (Show Source):
Question 239806: 2 logx= log(8x-160)+1
Answer by vleith(1977) (Show Source):
Question 239555: how do I solve the logarithmic equation: 7lnx=21?
Answer by Alan3354(6079) (Show Source):
Question 239430: log(x-1)+log(x+2)=log(14)
Answer by solver91311(5072) (Show Source):
Question 239299: Find domain:
f(x)= log(x^2-7x+6)
f(x)= ln(log(2x+4))
f(x)= square root of (1-x^2)/x
[Square root is only for numerator]
Evaluate:
log -2(-2 subscript) square root of 4
Answer by edjones(3295) (Show Source):
You can put this solution on YOUR website!f(x)= log(x^2-7x+6)
x^2-7x<=6 This is not allowed.
x^2-7x-6<=0
.
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=73 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 7.77200187265877, -0.772001872658765.
Here's your graph:
 | |
.
The domain is x(-infinity, (7-sqrt(73))/2) U ((7+sqrt(73))/2, infinity)
.
Ed
Question 239170: solve without using a calculator: 3ln(3x)=9
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!
Divide both sides by 3:
Use the fact that is equivalent to  to rewrite the logarithmic equation in exponential form:
Divide both sides by 3:
This is an exact answer and it may be the desired answer. We could also substitute for e (using the approximation 2.7183 which we could find without a calculator):
I'll leave it up to you to simplify this.
Question 239135: 10^(2-5x)=793 please solve without a calculator
Answer by jsmallt9(591) (Show Source):
You can put this solution on YOUR website!
As far as I can tell, 793 is not an integral power of any integer. So the only way I know how to solve for x is to find the base 10 logarithm of each side:
Now we can use the property of logarithms,  , to move the exponent in the argument in front:
and since the log(10) = 1 (This is why I chose base 10 logarithms):
Now that x is no longer in an exponent we can use basic Algebra to solve for it. Add -2 to (or subtract 2 from) each side:
Divide both sides by -5:
or
If "without calculators" means you are allowed to use tables of logarithms instead (Do textbooks come with tables of logarithms in the back anymore?), then we could do the following:
Factor out 100 from 793:
Use the property of logarithms, , to split the 100 and 7.93:
Since  ,  :
By factoring out the 100, we now have a logarithm we can find in a table:
I'll leave this to you to simplify.
If you are not supposed to use a table, I do not see another way to get rid of the logarithm in
All we can do is manipulate the expression into possibly more desirable forms. As we saw before  so we substitute for the 2:
Now we can use the property of logarithms,  , to combine the logarithms in the numerator:
We can change the division by 5 into the multiplication by its reciprocal, 1/5:
Then we can use the previously used property involving exponents, , to move the number in front into the argument as an exponent:
Writing the fractional exponent in radical form we get:
Which is a "better" answer?
or
I can't say for sure. I prefer the first one.
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