Question

Solve the following equation:
$5^x-24=\frac{25}{5^x}$

Answer 1

Let $5^x$ be $t,t>0$

$5^x-24=\frac{25}{5^x}$

$t-24=\frac{25}{t}$

$t^2-24t-25=0$

$(t-25)(t+1)=0$

$t=25$ or $-1$

$t=25$

$5^x=25$

$5^x=5^2$

$x=2$