# Logarithm problem

Gold Member
I am not very good in logs i have tried to attempt below problem in vain..give me an insight.
Prove Log(√27 + Log √8 - Log √125 ) / (Log 6 – Log 5) =3/2
I am not good in logarithms how do you show this…
This is how I did it:,
Log ( ( 3√3 *2√2 ) / 5√5 ) ) / ( 6/5)

((3√(3 *) 2√2 *5)) / ((5√5 *6)) = 6/5 and not 3/2 as indicated by problem am i right?

Last edited:

Is it log10 or the natural logarithm?

Are you sure the problem is correctly written in your post. If you include more parentheses it would be somewhat clearer.

You are expected to use:

log(ab) = log(a) + log(b)
log(a^b) = b log(a)

as well as some factorizing and shortening of fractions.

I checked the numerical value by typing it into Octave, but didn't get 3/2 or 6/5, not with log10 and not with the natural logarithm :-) I won't garantee that I did nothing wrong, though.

Gold Member
Is it log10 or the natural logarithm?

Are you sure the problem is correctly written in your post. If you include more parentheses it would be somewhat clearer.

You are expected to use:

log(ab) = log(a) + log(b)
log(a^b) = b log(a)

as well as some factorizing and shortening of fractions.

I checked the numerical value by typing it into Octave, but didn't get 3/2 or 6/5, not with log10 and not with the natural logarithm :-) I won't garantee that I did nothing wrong, though.

This is a logarithms used in every day calculations i.e of base 10 and they are reffered to as common logarithms and the base 10 is often omitted...kindly note that the question is to be solved without the help of tables or other....the solution to the problem is 3/2
kindly solve manually showing your steps i have shown mine...i am conversant with the laws of logarithms.

Mentallic
Homework Helper
I am not very good in logs i have tried to attempt below problem in vain..give me an insight.
Prove Log(√27 + Log √8 - Log √125 ) / (Log 6 – Log 5) =3/2
I am not good in logarithms how do you show this…
This is how I did it:,
Log ( ( 3√3 *2√2 ) / 5√5 ) ) / log ( 6/5)

Fixed.

You're trying to solve $$\frac{\log\left(\frac{3\sqrt{3}\cdot 2\sqrt{2}}{5\sqrt{5}}\right)}{\log\left(\frac{6}{5}\right)}$$

((3√(3 *) 2√2 *5)) / ((5√5 *6)) = 6/5 and not 3/2 as indicated by problem am i right?

$$\frac{log(a)}{log(b)}\neq \frac{a}{b}$$ so I'm not surprised it doesn't give you the answer you were looking for.

Look at the numerator, simplify the part inside the log, and then convert the roots into fractional powers to make things clearer

p.s. It doesn't matter what logarithm it is. The answer is independent of this.

Gold Member
Log (3^3/2 * 2^3/2 / 5^3/2) = Log (6/5)

Log (3*2/5)^3/2 = Log (6/5)

Log (6/5)^3/2 = Log (6/5)
3/2 Log (6/5) = Log (6/5)
3/2 = log (6/5) / Log (6/5)
=3/2
I love physics forum thank you so much…….maths for life
thanks a lot mentallic.

Mentallic
Homework Helper
No worries