# Questions on Algebra: Logarithm answered by real tutors!

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Question 994412: how to calculate log e with base 144 using tables
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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:
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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.

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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)
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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)
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if

=>=>=>
then

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

=
=

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

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

=     ----->

=     ----->

=                     ----->

x = = 0.6561.

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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!

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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.
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(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.

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You want to simplify the expression,

Change Of Base Formula gives

Next deal with the denominator,

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)

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.

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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:
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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):
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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
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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 = ?

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John

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

Question 992285: log 2.718 ?
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John

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

Question 991863: Please solve the equation for x : e^(x+1) = 100

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

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.
(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

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.
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
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.
+ + + . . . . . 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:
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Log9 tanπ/6
 =  =
=



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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.

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.
Makes no sense.

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

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.
= .

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

x + 1 = 50x + 25,

49x = -24,

x = .

Question 991383: 2log2+log150-log6 in base 10
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.
2log2+log150-log6 in base 10
-----------------------------------

+ - = = = 2.

Question 991107:
1.Solve
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

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:
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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.

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Is this it:

If so,

Hope I got it

Question 990843: solve for x. 40(1.05)^x=200

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

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Solve each equation for x. ln(x+3)+ln(x-3)=ln27
    OR      x = - 6 (ignore)



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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

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.
+ = .     ----->

= ,

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

x + 3 = 27x - 81,

26x = 78,

x = = 3.

Question 990648: when will three different time watches show the same time?
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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)

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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

Question 990457: True or false: Inx/Iny = In(x-y) Justify
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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)

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.
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

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

OK

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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)