## anonymous 5 years ago how do you make the bases of a logarithm the same?

1. amistre64

can you give more detail?

2. anonymous

^ i was thinking the same ^

3. anonymous

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 $a = b^k \iff log_b(a) = k$ $\therefore log_b(a) = \frac{log_q(a)}{log_q(b)} \forall a,b,q \in R$