Question

Logarithms - Please Help!!!

Which of the following is equivalent to log5(m)/log15(m)?

Choose 1 answer.

A) 1/3

B) 3

C) log(3)

D) log5(15)

Answer 1

D) log5(15)

Explanation:

The relevant rule of logarithms is called the "change of base formula:"

`\log_b(a)=(\log(a))/(\log(b))`

The logs on the right side of this equation can have any base, provided both have the same base.

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Your expression can be simplified as follows:

`(\log_5(m))/(\log_(15)(m))=(\left((\log(m))/(\log(5))\right))/(\left((\log(m))/(\log(15))\right))=(\log(15))/(\log(5))=\boxed{\log_5(15)}`