Question

What is the value of x if 9^(x-1)-2=25

Answer 1

$\bf 9^{x-1}-2=25\implies 9^{x-1}=25+2\implies 9^{x-1}=27\quad \begin{cases} 9=3^2\\ 27=3^3 \end{cases} \\\\\\ (3^2)^{x-1}=3^3\implies 3^{2(x-1)}=3^3\impliedby \begin{array}{llll} \textit{base is the same, thus}\\ \textit{exponents are the same} \end{array} \\\\\\ 2(x-1)=3\implies x-1=\cfrac{3}{2}\implies x=\cfrac{3}{2}+1\implies x=\cfrac{5}{2}$