Finding log

Question

If log_a20=b and log_a5=c, find log_a2

I need help, I just don't understand...

The answer is supposed to be like c-b, b+c, or something like that...

Please, your help is really appreciated. 

Answer 1

Hi Javier,

 

This takes some trial and error and an understanding of the properties of logarithms.

 

We do know that "the log of a quotient equals the difference of the logs".

 

So perhaps log_a20/5 = log_a20 - log_a5 will lead somewhere. Notice that the log_a20/5 = log_a4. 

 

The log_a4 = log_a2² = 2log_a2 (another property of logs).

 

Putting that all together we have log_a20 - log_a5 = 2log_a2.

 

Substituting what is given we have: b - c = 2log_a2. Or, log_a2= (b-c)/2