Question

Solve for $x$ : $2^{5x-1}=4\times 2^{3x+1}$

Answer 1

We have $2^{5x-1}=4\times 2^{3x+1}$
$=>2^{5x-1}=2^2\times 2^{3x+1}$
By using law $a^m\times a^n=a^{m+n}$
$\therefore 2^{5x-1}=2^{3x+1+2}$
As base is same, we can equate the powers
$\therefore 5x-1=3x+3$
$=>5x-3x=3+1$
$=>2x=4$
$=>x=2$