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lutik1710 [3]
3 years ago
6

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

Mathematics
1 answer:
Lina20 [59]3 years ago
6 0
\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}
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