Question

If ${25}^{(x-1)}=5^{(2x-1)}-100$ then find the value of x.

Answer 1

${25}^{(x-1)}=5^{(2x-1)}-100$
$\therefore \frac{{25}^x}{25}=\frac{{25}^x}{5}-100$
$\therefore {25}^x(\frac{1}{25}-\frac{1}{5})=-100$
${25}^x\left(\frac{1-5}{25}\right)=-100$
$\therefore {25}^{x-1}(-4)=-100$
${25}^{x-1}=25$
$\therefore x-1=1$
$\therefore x=2$