Question

If (4)^2x-1 - (16)^x-1 = 384, find the value of x.

Answer 1

Given (4)^(2x - 1)  -  (16)^(x - 1) = 384

$= \ \textgreater \ (4)^{2x - 1} - (4^2)^{x - 1} = 384$

$= \ \textgreater \ 4^{2x} . 4^{-1} - 4^{2x} * 4^{-2} = 384$

$= \ \textgreater \ 4^{2x} ( 4^{-1} - 4^{-2} ) = 384$

$= \ \textgreater \ 4^{2x} = \frac{384}{ 4^{-1} - 4^{-2} }$

$= \ \textgreater \ 4^{2x} = \frac{384}{ \frac{1}{4} - \frac{1}{16} }$

$= \ \textgreater \ 4^{2x} = \frac{384}{ \frac{3}{16} }$

$= \ \textgreater \ 4^{2x} = \frac{384 * 16}{3}$

$= \ \textgreater \ 4^{2x} = 2048$

$= \ \textgreater \ (2^2)^{2x} = 2^{11}$

$= \ \textgreater \ 2^{4x} = 2^{11}$

$= \ \textgreater \ 4x = 11$

= > x = 11/4.



Hope this helps!