Let ()=log() where we don't know the base .

Question

Let ()=log() where we don't know the base .

However, we do know that (2)=0.37031 and (3)=0.58692

Use this information to compute

(4)=

(^2)=

(^3)=

(6^5)=

I tried to do 0.37031=log2 and 0.58692=log3 and convert both to exponential form but I'm not sure how to find the base value. Any tips on how to properly start this question would be appreciated!

Answer 1

Just do it.

You know $\log_a b^m = m\log_a b$ so you can use this to solve $L(4) = \log_a 2^2$.

And you know $\log_a a^k = k$ which you can use to solve the next two.

And you know $\log_a bc = \log_a b + \log_a c$ which you can use to solve the last one.