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

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

Mathematics
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can you give more detail?
^ i was thinking the same ^
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 \[a = b^k \iff log_b(a) = k\] \[\therefore log_b(a) = \frac{log_q(a)}{log_q(b)} \forall a,b,q \in R\]

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