Question

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

Answer 1

`5^(2x)+7*5^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`