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lozanna [386]
3 years ago
9

Solve for x: 5^2x + 7(5^x) - 18

Mathematics
1 answer:
77julia77 [94]3 years ago
3 0
5^{2x}+7\times5^x-18=\left(5^x+9\right)\left(5^x-2\right)

I'm assuming this is set equal to zero (just to make things easy). Then you have

\begin{cases}5^x+9=0\\5^x-2=0\end{cases}\implies\begin{cases}5^x=-9\\5^x=2\end{cases}

The first equation has no solution, since 5^x is always positive.

Meanwhile,

5^x=2\implies \log_55^x=\log_52\implies x=\log_52
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