1=(a)log(4)+(a)log(2) , can I factor out a then combine the logs and divide by the logs?

Question

Am I able to do this?
1=(a)log(4)+(a)log(2)
1=a(log(4)+log(2))
1=a(log(8))
a=1/log(8)

Answer 1

Hi,

Your answer is perfectly fine. Excellent job. Yes, factor out then make sure the logs are of the same bases. Here the logs are of base 10, so you can combine them (product rule). However, your answer can still be simplified since 8 is 2³. 

So, the final answer should be a=1/(3*log2)