Question

Log 144 ko log2 aur log3 ke term me likho

Answer 1

First take the prime factorization of 144.

$\begin{tabular}{c|l}2&144\\ \cline{2-}2&72\\ \cline{2-}2&36\\ \cline{2-}2&18\\ \cline{2-}3&9\\ \cline{2-}&3\\ \cline{2-}\end{tabular}$

$\therefore\ 144=2^4\times 3^2$

So,

$\log(144)\ =\ \log(2^4\times 3^2)\ =\ \log(2^4)+\log(3^2)\ =\ \bold{4\log(2)+2\log(3)}$

That's all!

Identities used:

$1.\ \ \log(a\times b)\ =\ \log(a)+\log(b)\\ \\ 2.\ \ \log(a^b)\ =\ b\log(a)$