Question

Hey!! friends
plzz....solve the above question!!

how to solve after that step I'm stuck ?

$<Marquee>$

$\boxed{\colorbox{teal}{Anyone plz answer fast}}$

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}}$



$\sf = log_p \: \left( log_p \: \sqrt[p]{\sqrt[p]{ \sqrt[p]{ \sqrt[p]{ \sqrt[p]{p..... \: n \: times} } } }} \right) \\ \\ \\ \sf = \: log_p \: \left( log_p \: {p}^{ \normalsize{\frac{1}{ {p}^{n} } }} \right) \\ \\ \\ \sf = log_p \: \left( \dfrac{1}{ {p}^{n} } \:log_p \: p \right) \\ \\ \\ \sf = log_p \: \left ( \dfrac{1}{ {p}^{n} } \: \times \: 1\right) \\ \\ \\ \sf = \: log_p \: \: \left(\dfrac{1}{ {p}^{n} } \right) \\ \\ \\ \sf = \: log_p \: {p}^{( - n)} \\ \\ \\ \sf = ( - n) \: log_p \: p \\ \\ \\ \sf = ( - n) \: \times \: 1 \\ \\ \\ \sf = - n$




$\underline{\textsf{Logarithm Rule Used : }} \\ \\ \sf \implies log_a \: b^c \: = \: c \: log_a \: b \\ \\ \sf \implies log_a \: a \: = \: 1 \\ \\ \underline{\textsf{Algebraic Identity Used : }} \\ \\ \sf \implies \dfrac{1}{a^n} \: = \: a^{(-n)}$