Question

(2^2x+3) - (2^x-3) = 126 then find the value of x​

Answer 1

$2^{2x+3}-2^{x-3} = 126$

$2^{2x}*2^3 - 2^x*2^{-3} = 126$

$2^{x^2}*2^3 - 2^x*2^{-3} = 126$

Let $2^x = a$

Hence

$a^2*8 - \frac{a}{8} = 126$

Multiplying throughout by 8, we get

$64a^2 - a = 1008$

$64a^2 - a - 1008 = 0$

$a = \frac{-(-1)+\sqrt{(-1)^2-4*64*(-1008)} }{2*64}$  OR  $a = \frac{-(-1)-\sqrt{(-1)^2-4*64*(-1008)} }{2*64}$

a = 3.9764 OR a = -3.9608 (rejected)

$2^x = a$

Applying logarithm on both sides

$xlog2 = loga$

$x = \frac{loga}{log2}$

$x=\frac{loga}{0.3010}$

$x = \frac{log(3.9764)}{0.3010}$  

$x = 1.9917$  

This is an approximated value

HOPE IT HELPS !!