Question

What is the value of log root to base 3 root5​

Answer 1

We have,

\log _5({\sqrt[3]{5})

To find, the vaue of \log _5({\sqrt[3]{5})=?

∴ \log _5({\sqrt[3]{5})

=\dfrac{\log\sqrt[3]{5})}{\log 5}

[ ∵ \log _x(a)=\dfrac{\log a}{\log x}]

=\dfrac{(\log 5^{\dfrac{1}{3} } )}{\log 5}

=\dfrac{1}{3} \dfrac{\log 5}{\log 5}

=\dfrac{1}{3}

=0.333

Hence, the value of \dfrac{1}{3} \dfrac{\log 5}{\log 5}=0.333