What rules are we using to show that $3^{-s}=\frac{1}{2}$ if $s=\frac{\log 2}{\log 3}$

I cannot understand how you can raise a number to a logarithm divided by a logarithm


Applying the rule for change of bases, observe first that $\log_3 2 = \frac{\log 2}{\log 3}= s$, where the latter logarithms (in the ratio) can be to any base (but identical in numerator and denominator).

Then $3^{-s} = \frac{1}{3^s} = \frac{1}{2}$

because $3^{\log_3 2} = 2$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.