Question

solve.............................

Answer 1

$log_{ {a}^{q} }( {m}^{p} ) \\ \\ as \: we \: know \: formula \: \\ log( { a}^{b} ) = b \: log(a) \\ \\ log_{a}(b) = \frac{ log(b) }{ log(a) } \\ \\ \\ log_{ {a}^{q} }( {m}^{p} )= \: p \: log_{ {a}^{q} }(m) \\ = p \: ( \frac{ log(m) }{ log( {a}^{q} ) } ) \\ = p \: \frac{ log(m) }{ qlog(a) } \\ = \frac{p}{q} ( \frac{ log(m) }{ log(a) } ) \\ = \frac{p}{q} log_{a}m$

answer is option i