Question

how do you make the bases of a logarithm the same?

Answer 1

can you give more detail?

Answer 2

^ i was thinking the same ^

Answer 3

I'm guessing you have a situation where you've got logs with mixed bases in some equation. In this situation, you can use the change of base formula.

\[\text{Let } a = b^k,\text{ and }q \in R\]\[\implies log_q(a) = k\cdot log_q(b)\]
\[\implies k = \frac{log_q(a)}{log_q(b)}\]
From the definition of the logarithm we also have that
\[a = b^k \iff log_b(a) = k\]
\[\therefore log_b(a) = \frac{log_q(a)}{log_q(b)} \forall a,b,q \in R\]