# Logarithm Proof

1. Dec 1, 2008

### ElementUser

1. The problem statement, all variables and given/known data

Prove:

1/log3a + 1/log4a = 1/log12a

2. Relevant equations

ay=x
Logarithms rules (addition, subtraction, power, etc.)

logax=logbx/logba

3. The attempt at a solution

Left Side:

1/log3a + 1/log4a
=log3a+log4a/log12a (via common denominator)

The problem is how to add logarithms with different bases. I tried converting the log3a to log4a (I get log4a/log43). After that, I subbed it back into the equation.

=log4a/log43+log4a

But I don't think that gets me anywhere...

Right side still remains the same (1/log12a)

Any help is appreciated! Thanks in advance :).

P.S. What program do people use to make their equations look so neat (the fraction looks real - ex. 1/4 really looks like 1 (horizontal line) 4)?

2. Dec 1, 2008

### Dick

Let's just convert everything to a single log base, like log_12. E.g. log_3(a)=log_12(a)/log_12(3).

3. Dec 1, 2008

### ElementUser

Oh, wow. Sigh, I hate it when you take the wrong approach in proving Left Side equals Right Side.

Thanks for the help! Can't believe it was so simple after your suggestion :).