Question

Proof ,

$log_{a}(b) = x$

Answer 1

$<h2><font color = red > hey there$



$<font color = black > here we go....$


$log_{a}(b) = x$



$a {}^{x} = b$



$a {}^{ \frac{x}{x} } = b {}^{ \frac{1}{x} }$



$a = b {}^{ \frac{1}{x} }$



$log_{a}(b) = \frac{1}{x}$



$x = \frac{1}{ log_{b}(a) }$



Hope it helps you

Thanks for asking........



$<b > prabhudutt$

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

$<h2><b><i><font face=Copper black size=4 color=blue>$

Here is your answer

$log_{a}(b) = x \\ \\ {a}^{x} = b \\ \\ {a}^{x \times \frac{1}{x} } = {b}^{ \frac{1}{x} } \\ \\ {a}^{ \frac{x}{x} } = {b}^{ \frac{1}{x} } \\ \\ a = {b}^{ \frac{1}{x} } \\ \\ log_{a}(b) = \frac{1}{x} \\ \\ x = \frac{1}{ log_{b}(a) }$

Hence,

$log_{a}(b) = x = \frac{1}{ log_{b}(a) }$
Hence, Proved

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\: helps\: you}}}}}}}}}}}}}}}$