Question 193715
*[Tex \LARGE \log_{4}\left(\sqrt{64}\right)] ... Start with the given expression.



*[Tex \LARGE \log_{4}\left(8\right)] ... Take the square root of 64 to get 8.



*[Tex \LARGE \frac{\log_{10}\left(8\right)}{\log_{10}\left(4\right)}] ... Break the log using the change of base formula.



*[Tex \LARGE \frac{\log_{10}\left(2^3\right)}{\log_{10}\left(2^2\right)}] ... Rewrite {{{8}}} as {{{2^3}}}. Rewrite {{{4}}} as {{{2^2}}}. 



*[Tex \LARGE \frac{3\log_{10}\left(2\right)}{2\log_{10}\left(2\right)}] ... Pull down the exponents.



*[Tex \LARGE \frac{3}{2}] ... Cancel out the common terms.



So *[Tex \LARGE \log_{4}\left(\sqrt{64}\right)=\frac{3}{2}]