Math joke for i love math

$Exercise\,\, 1:\,\,Solve\,\, the\,\, following\,\, inequality,\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\log\sqrt[t]{\frac{i}{3m}}<\frac{h}{\log_{a}{10}}\\

Solution:\,\, we\,\, know\,\, that,\,\,\sqrt[t]{w}=\left ( w \right )^{\frac{1}{t}},then\\


\log\sqrt[t]{\frac{i}{3m}}=\log\left ( \frac{i}{3m} \right )^{\frac{1}{t}}
=\frac{1}{t}\log\left ( \frac{i}{3m} \right )<\frac{h}{\log_{a}{10}}

\\

but \log_{a}{10}=\frac{\log 10}{\log a}\,\, then \frac{h}{\log_{a}10} =\frac{h}{\frac{\log10}{\log a}}=h\log a \\

hence,\,\,\log\left ( \frac{i}{3m} \right )<\log a^{th}\\


Thus,\,\,i<3\,\,ma^{th}$