Question

$find \: the \: value \: of \: log_{7} \sqrt{343}$
please solve it urgently​

Answer 1

$log_{7}( \sqrt{343} )$

$\implies log_{7}( \sqrt{ {7}^{3} } )$

$\implies log_{7}( {7}^{ \frac{3}{2} } )$

$\sf{ \purple{since : }}$

$\red{ \boxed{ log( {a}^{m} ) = m log(a) }}$

$\implies \frac{3}{2} \times log_{7}(7)$

$\red{ \boxed{ log_{a}(a) = 1}}$

$\implies \frac{3}{2} \times 1$

$\orange{\therefore log_{7}( \sqrt{343} ) = \frac{3}{2} }$