l o g 5 10 + l o g 5 2 3 + l o g 5 64 {\displaystyle {\frac {log_{5}{10}+log_{5}2}{3+log_{5}{64}}}}
l o g 5 10 + l o g 5 2 3 + l o g 5 64 l o g 5 2 ∗ 5 + l o g 5 2 3 + l o g 5 2 6 log a ( x ⋅ y ) = log a ( x ) + log a ( y ) l o g 5 2 + l o g 5 5 + l o g 5 2 3 + l o g 5 2 6 log a ( 1 ) = 0 2 ∗ l o g 5 2 + 1 3 + l o g 5 2 6 log a ( x n ) = n ⋅ log a ( x ) 2 ∗ l o g 5 2 + 1 3 + 6 l o g 5 2 1 + 2 l o g 5 2 3 ( 1 + 2 l o g 5 2 ) = 1 3 {\displaystyle {\begin{aligned}{\frac {log_{5}{10}+log_{5}2}{3+log_{5}{64}}}\\{\frac {log_{5}{2*5}+log_{5}2}{3+log_{5}{2^{6}}}}\\{\displaystyle \log _{a}(x\cdot y)=\log _{a}(x)+\log _{a}(y)}\\{\frac {log_{5}{2}+log_{5}5+log_{5}2}{3+log_{5}{2^{6}}}}\\{\displaystyle \log _{a}(1)=0}\\{\frac {2*log_{5}{2}+1}{3+log_{5}{2^{6}}}}\\{\displaystyle \log _{a}(x^{n})=n\cdot \log _{a}(x)}\\{\frac {2*log_{5}{2}+1}{3+6log_{5}{2}}}\\{\frac {1+2log_{5}{2}}{3(1+2log_{5}{2})}}\\={\frac {1}{3}}\end{aligned}}}
![{\displaystyle {\displaystyle log_{a}({\sqrt[{n}]{x}})={\frac {1}{n}}log_{a}x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e938813e87e14b2f468c2da2fc8f99b57d92bafe)
