Question

Solve for $x$
$5^{-3x}:5^{x+7}=1:125$

Answer 1

We have,

$5^{-3x}:5^{x+7}=1:125$

$\frac{5^{-3x}}{5^{x+7}}=\frac{1}{125}$

$\frac{1}{5^{x+7+3x}}=\frac{1}{5^3}$

$\frac{1}{5^{4x+7}}=\frac{1}{5^3}$

$5^{4x+7}=5^3$

On comparing both sides, we get

$4x+7=3$

$4x=-4$

$x=-1$

Hence, this is the answer.