# Questions on Algebra: Logarithm answered by real tutors!

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Question 994412: how to calculate log e with base 144 using tables
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
how to calculate log e with base 144 using tables
-------------
If you mean

= ln(e)/ln(144)
= 1/ln(144)

Question 994061: 7Inx-3(Inx^3+5inx)

solve as a single logarithm. I am stuck on this problem, I have been working on it for an hour.

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
7Inx-3(Inx^3+5inx)

solve as a single logarithm. I am stuck on this problem, I have been working on it for an hour.
=============
It's not "solve"
Just rewrite, as the other tutor did.
-----------
PS It's LN, for natural log, not IN.

Answer by stanbon(69061)   (Show Source):
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7Inx-3(Inx^3+5inx)
-----
ln(x^7) - 3( ln(x^3) + ln(x^5))
-----
ln(x^7) -3ln(x^3) -3ln(x^5)
-----
ln(x^7) -ln(x^9) - ln(x^15)
-----
ln[x^7/(x^9*x^15)]
-----
ln[x^7/x^24]
----
ln[x^-17]
=====
= -17ln(x)
==============
Cheers,
Stan H.
==============

Question 993984: if log 3=a log 4=b find log(root18)
Answer by fractalier(2141)   (Show Source):
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If b = log 4, then b = 2 log 2 or log 2 = b/2.
Then
log sqrt(18) = (1/2) log (18) = (1/2) log (2 x 3^2) =
(1/2) [log 2 + 2 log 3] =
(1/2)(b/2) + a =
a + b/4

Question 993985: when log3=a log4=b Find log(root18)
Answer by MathLover1(11324)   (Show Source):
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if

=>=>=>
then

=
=
=
=...since and , we have

=
=

Question 993977: if log 3=a log 4=b find log15

Answer by stanbon(69061)   (Show Source):
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if log 3=a log 4=b find log15
---
log(15) = log(3*5) = log(3) + log(20/4)
---
= log(3) + log(2) + log(10) - log(4)
------
= a + b/2 + 1 - b
----
= a - (b/2) + 1
--------------------
Cheers,
Stan H.
----------

Question 993715: log2(x+2)-log2(x)=3
Answer by ikleyn(988)   (Show Source):
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.
- = .       ----->

= .             ----->

= =           ----->

x + 2 = 8x,

and so on.

Question 993545: 4logbase10(0.9)=logbase10(x)
calculate the value of x with full method show

Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(988)   (Show Source):
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.
4logbase10(0.9)=logbase10(x)
calculate the value of x with full method show.
-----------------------------------------------------

=     ----->

=     ----->

=                     ----->

x = = 0.6561.

Answer by josgarithmetic(13975)   (Show Source):
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Electronic calculator or table of logarithms.

-------this text did not render, so,

Question 993335: Hello,
trying to find out how to get the result of given:
Titer sample #1 = 53 * (e 3.2 * 0.852) = 53 * 15.28 = 810
so the answer is 810. how they get 15.28?
Thank you!

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
trying to find out how to get the result of given:
Titer sample #1 = 53 * (e 3.2 * 0.852) = 53 * 15.28 = 810
so the answer is 810. how they get 15.28?
===============

Question 993392: (2logy+1)³. y is base of log and 1 is another term. This is correct question as it is.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
(2logy+1)³. y is base of log and 1 is another term. This is correct question as it is.
--------------
If you mean
log(1) = 0 (with any base > 0)
----

Question 993329: Given x = log_b 8 , y = log_b 3, I have to express the answer in terms of x and y.
log_3b (8/9) is the given equation.
I got up to log_3b 8 - 2 log_3b 3, currently wondering how do I change the base 3b to b, but the base is a variable so I'm not sure how to do so.

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!

You want to simplify the expression,

Change Of Base Formula gives

Substitute your given relationships,

Next deal with the denominator,

Question 993277: please help me convert this equation into log form: 8(10)^(6x+5)=40
Answer by Edwin McCravy(13211)   (Show Source):
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Instead of doing yours for you, here's an example
exactly like yours step by step.  Use it as a model.

Divide both side by 7

Use the definition of common logs:

is equivalent to

Get a calculator:

Now do yours exactly the same way.

Edwin

Question 992958: simplify andexpress each of the following as a single log
i)lg (8/75)-2 lg(3/5)+4 lg(3/2)
ii)2 log (x+2)+log (x+1)-log (x^2 +3x+2)

Answer by MathLover1(11324)   (Show Source):

Question 992730: I think this question requires logarithms
Given the equation y=a*b^x find the values of a and b for the curve that passes through the points (-2, 1) and (2,5)
Sorry if it's the wrong section, but I don't really know what to do.

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Your model in general is useful also for the logarithms of its left and right side
members.
Choose either base 10 or e. Here will be using base 10.

You now want to adjust your given points to use instead of the y coordinates as given
because that is how the equation has been treated. Your points to use in the green-outlined equation
must now be (-2, log(10,1)) and (2, log(10,5)).
Those points, if decimal form will help, (-2,0) and (2,0.6990).
-
Again, these points are for the LINEAR equation outlined in green - NOT for the original model
of .

Now you have the two points, treated for their logarithms of y, and you can find the
vertical axis intercept which is and the slope which is .
That allows you to find a and b.

Question 992596: por favor me pueden ayudar con el desarrollo de todo el procediemiento de la funcion .f(x)=log(3-x) todo el paso a paso gracias
Found 2 solutions by AnlytcPhil, Edwin McCravy:
Answer by AnlytcPhil(1539)   (Show Source):
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f(x)=log(3-x)

Logarithms must have a base either understood or written.

Do you mean logarithm with base 10?

log10(3-x)

Or logarithm with base 2, 3, 4, etc.?

log2(3-x), log3(3-x), log4(3-x)?

Or do you mean logarithm with base

e = 2.718281828459045235360287471352662497757247...?

loge(3-x) which we usually write with ln(3-x)

The graph of log10(3-x) is as follows:

Edwin

Answer by Edwin McCravy(13211)   (Show Source):
You can put this solution on YOUR website!
f(x)=log(3-x)

Logaritmos deben tener una base bien
entendido o por escrito.

¿Te refieres a logaritmo con base 10?

log10(3-x)

¿O logaritmo con base 2, 3, 4, etc..?

log2(3-x), log3(3-x), log4(3-x)?

¿O te refieres a logaritmo con base

e = 2.718281828459045235360287471352662497757247...?

que usualmente escribimos con "ln".

La gráfica es como sigue:

Edwin

Question 992578: por favor me ayudan con todo el desarrollo de la funcion . f(x)=log (3-x) gracias
You can put this solution on YOUR website!
Desarrollo de que... la derivativa? Si es esto me avisas y te la mando. Si es otra cosa, vuelve a subir tu pregunta pero por favor especifica lo que necesitas.

Question 992322: 1> If log 2 base 10 = 0.8010 , then log 10 base 2 = ?
2> If log 2 = 0.3010 , then log 5 = ?

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Question 992285: log 2.718 ?
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Question 991863: Please solve the equation for x : e^(x+1) = 100
Answer by Fombitz(25151)   (Show Source):

Question 991815: 1. Prove that. (I) log3. Log2. Log√3 81=1
(ii) Logax X logby = Logbx X logay
(iii) log2. Log2. Log2 16=1

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
(iii) log2. Log2. Log2 16=1
--------------------------------------

The statement is: = 1.

Proof: =         (since = 4)

=                   (since = 2)

= 1.

Question 991814: 1. 1/log2a+1/log4a+1/log8a+.....upto n term
2. Loga2b+log√a(b)2
3. Log√5•008
4. Log2√3 144

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Hello,
#1 is just solved, see this link
http://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.991818.html

Question 991818: 1/log2a+1/log4a+1/log8a+......upto n term
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
+ + + . . . . . upto n term
-------------------------------------------------------------------------

Notice that

= .

It is the consequence of the  "base change formula"  for logarithms  (see any  Algebra  textbook or the lesson  Change of Base Formula for logarithms  in this site).

Therefore,  we can re-write the formula in the form

+ + + . . . + = + + + . . . +

Next,  notice that    = ,    = , . . . ,    = .

Thus you have,  actually,  the sum

+ + + . . . + = .(1 + 2 + 3 + . . . +n),

which is equal to   ..

Answer.  The sum is equal to  . = ..

Thank you for submitting so exciting problem.

Question 991796: Log9 tanπ/6
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(4047)   (Show Source):
You can put this solution on YOUR website!

Log9 tanπ/6
 =  =
=



Answer by ikleyn(988)   (Show Source):
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.
= .

Therefore, = = .

Question 991501: Given log 2=p log 7=q
Find (14^3x+1)(8^2x+3)=7 in terms of p and q.

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Makes no sense.

Question 991386: 2log2+log150-log6 in base 10
Lig5(x+1)-Log5(2x+1)=2. What is x?

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
= .

x+1 = 25(2x+1),

x + 1 = 50x + 25,

49x = -24,

x = .

Question 991383: 2log2+log150-log6 in base 10
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
2log2+log150-log6 in base 10
-----------------------------------

+ - = = = 2.

Question 991107:
1.Solve
x^2+3x−4/2x^2+−3≤ 0, indicating your answer by interval notation.
2.Solve: log2 [log3 (2x+1)]=2 (Q2 p.s: log2and log3 2and3 are in small letter)
3.−4X^2 + |x| = −3
4.Simplify |cos x − 1|
5.Given that f(x) =1/1+log10x and g(x) =1/x^2
(iii) Find (f ∘ g)(x) and state its domain and range.
(a) Domain: (−∞, 0)⋃(0, ∞) Range: (−∞, ∞)
(b) Domain: (−∞, 0)⋃(0, ∞) Range: (−∞, 0)⋃(0, ∞)
(c) Domain: (−∞, −√10)⋃(−√10, 0)⋃(0,√10)⋃(√10, ∞)
Range: (−∞, ∞)
(d) Domain: (−∞, −√10)⋃(−√10, 0)⋃(0,√10)⋃(√10, ∞)
Range: (−∞, 0)⋃(0, ∞)
thanks so much

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Question 991094: How do you do this exercise:
logB = 3(log x -1) -2 (1 - log y)

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
logB = 3(log x -1) -2 (1 - log y)
----
I'll assume you want to solve for "y":
---
2(1-log(y)) = 3(log(x)-1) - log(B)
-----------
2 - 2log(y) = 3log(x) - 3 - log(B)
----------
-2log(y) = log(x^3/B) - 5
------------
log(y) = (5/2)-log[sqrt(x^3/B)]
-------
log(y) = (5/2) - log[x^(3/2)/B^(1/2)]
---
y = 10^[(5/2) - log[x^(3/2)/B^(1/2)]]
----------
Cheers,
Stan H.

Answer by josmiceli(13716)   (Show Source):
You can put this solution on YOUR website!
Is this it:

If so,

Hope I got it

Question 990843: solve for x. 40(1.05)^x=200
Answer by MathLover1(11324)   (Show Source):

Question 990762: Solve each equation for x. ln(x+3)+ln(x-3)=ln27
Found 4 solutions by brynmawr3, MathTherapy, solver91311, ikleyn:
Answer by brynmawr3(1)   (Show Source):
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The first answer by ikelyn is WRONG. MathTherapy got it right, x = 6.

Answer by MathTherapy(4047)   (Show Source):
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Solve each equation for x. ln(x+3)+ln(x-3)=ln27
    OR      x = - 6 (ignore)



Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Two rules: The sum of the logs is the log of the product, and if two logs of the same base are equal, then their arguments must be equal.

Discard any negative root because the domain of ln is the positive reals.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
+ = .     ----->

= ,

x + 3 = 27*(x - 3),

x + 3 = 27x - 81,

26x = 78,

x = = 3.

Answer.  x = 3.

Question 990648: when will three different time watches show the same time?
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Maybe never.

Question 990540: Please last i as this question but there was no response am asing it again
13log(25/4)-2log(4/5)+log(320/125)

Answer by Boreal(1464)   (Show Source):
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13log(25/4)-2log(4/5)+log(320/125)=
13 log 25-13 log 4-2 log 4+2 log 5+log 320-log 125=
13 log 25-log 125-15 log 4+2 log 5+ log 320.;;- a log with a denominator will be + for the denominator
13log 25-log 5^3-15 log 4+2 log 5+log (5*l64)
13 log 5^2-3 log 5-15 log 4+2 log 5+log 5+log 64
26 log 5-3 log 5-15 log 4 + 3 log 5+ log 4^3
23 log 5-15 log 4+3 log 5+3 log 4
26 log 5-12 log 4
also 26 log 5-12 log 2^2=26 log 5-24 log 2.
===
check numerically 18.17-7.22=10.95
====
13 log 6.25=10.35
-2 log (0.8)=+0.19
+log(320/125)=0.41
These add to 10.95

Question 990457: True or false: Inx/Iny = In(x-y) Justify
Answer by ikleyn(988)   (Show Source):
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.
True or false: Inx/Iny = In(x-y) ? Justify

1. When you operate with logarithms, use the symbol ln, not In.

2. Do not write Inx. Nobody will understand you. Write ln(x).

3. True or false: ln(x)/ln(y) = ln(x-y) ? ----- FALSE.

4. Justification? There is no any justification. Simply FALSE. Believe me.

Question 990459: Write as the logarithm of a single quantity:
1/5(3In(x+1)+2In(x-1)-In7)

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Write it step by step:
= = =

And one important note: when you operate with the logarithm, use ln as the symbol (not In).

Question 990289: What is the expanded form of ab in algebra
Answer by ikleyn(988)   (Show Source):

Question 990331: Solve log4 (m+2)-log4 (m-5)=log4 8
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(13716)   (Show Source):
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--------------
check:

OK

Answer by ikleyn(988)   (Show Source):
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.
- =

is

= .

So,  then

m + 2 = 8*(m-5), . . .

Would you complete it yourself?

Question 990249: use properties of logarithms to condense into the logarithm of a single quantity.
log2 (5) +7log2 (x)

Answer by lwsshak3(11500)   (Show Source):
You can put this solution on YOUR website!
use properties of logarithms to condense into the logarithm of a single quantity.
log2 (5) +7log2 (x)