Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can we say that $\log _4 (n^2)=\log _2(n)$? If that is the case, then $\displaystyle 2^{\log _4 (n^2)}=n$? Thanks.

share|improve this question
add comment

3 Answers

up vote 6 down vote accepted

Yes. Let $x=\log_4n^2=2\log_4n$; then $2^x=2^{2\log_4n}=\left(2^2\right)^{\log_4n}=4^{\log_4n}=n$.

share|improve this answer
    
Thanks, i will accept that in 10 minutes –  copy_constructor Mar 3 '13 at 15:19
    
@bigO: You’re welcome. –  Brian M. Scott Mar 3 '13 at 15:24
add comment

You can also prove this using the fact that $\log_a b =\dfrac{\log_c b}{\log_c a}$.

share|improve this answer
add comment

And more generally, $$ \log_b a = \log_{b^k} (a^k). $$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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