Question

Log 2 base x mines Log x base 4

Answer 1

$\log_{x}(2) - \log_{4}(x)$

$\implies \log_{x}(2) - \log_{4}(x)$

$\implies \log_{x}(2) - \log_{ {2}^{2} }(x)$

$\sf \purple{we \: know \: that}$

$\blue {\boxed { \sf \log_{ {b}^{m} }(a) = \frac{1}{m} log_{b}(a) }}$

$\implies \log_{x}(2) - \frac{1}{2} \log_{ {2} }(x)$

$\blue{ \boxed{ \sf \log_{a}(b) = \frac{1}{ log_{b}(a) } }}$

$\implies \log_{x}(2) - \frac{1}{2} ( \frac{1}{ \log_{x}(2) } )$

$\implies \log_{x}(2) - \frac{1}{2 \log_{x}(2) }$