Question

Evaluate................

Answer 1

recall that ln is just a shortcut for what really is logₑ, thus

`\bf \textit{Logarithm Cancellation Rules} \\\\ \boxed{log_a a^x = x}\qquad \qquad a^(log_a x)=x \\\\\\also~recall~that~~ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\ ln\left( \sqrt[5]{e} \right)\implies log_e\left( \sqrt[5]{e^1} \right)\implies log_e\left( e^{(1)/(5)}\right)\implies \cfrac{1}{5}`