Question

মান নির্ণয় কর: $\log_5\left(\sqrt[3]{5}\cdot\sqrt5\right)$

Answer 1

$\log_5\left(\sqrt[3]{5}\cdot\sqrt5\right)$

$=\log_5\left(5^{\frac13}\cdot5^{\frac12}\right)$

$=\log_5\left(5^{\frac13+\frac12}\right)$

$=\log_5\left(5^{\frac{2+3}{6}}\right)$

$=\log_55^{\frac56}$

$=\frac56\log_55$

$=\frac56\times1$

$=\frac56$ [Answer]