Question

find x if log 4 to the base x +log 16 to the base x =12​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1.

$log_{x}(y) + log_{x}(z) = log_{x}(yz)$

2.

$log_{x}( {y}^{m} ) = m log_{x}(y)$

TO DETERMINE

$x \: \: when \: \: log_{x}(4) + log_{x}(16) = 12$

CALCULATION

$log_{x}(4) + log_{x}(16) = 12$

$\implies \: log_{x}(4 \times 16) = 12$

$\implies \: log_{x}(64) = 12$

$\implies \: {x}^{12} = 64$

$\implies \: {x}^{12} = {( \sqrt{2}) }^{12}$

$\therefore \: x = \sqrt{2}$