rules for evaluating powers of logarithms What rules are we using to show that 3^(-s)=1/2 if s=(log 2)/(log 3) I cannot understand how you can raise a number to a logarithm divided by a logarithm

Deja Bradshaw

Deja Bradshaw

Answered question

2022-10-12

rules for evaluating powers of logarithms
What rules are we using to show that 3 s = 1 2 if s = log 2 log 3
I cannot understand how you can raise a number to a logarithm divided by a logarithm

Answer & Explanation

Plutbantonavv

Plutbantonavv

Beginner2022-10-13Added 15 answers

Applying the rule for change of bases, observe first that log 3 2 = log 2 log 3 = s, where the latter logarithms (in the ratio) can be to any base (but identical in numerator and denominator).
Then 3 s = 1 3 s = 1 2
because 3 log 3 2 = 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?