Question

If 9 raised to the power x+2 = 240 + 9 raised to the power x
Find x

Answer 1

$Given : 9^{x + 2} = 240 + 9^x$

$= \ \textgreater \ 9^{x + 2} - 9^x = 240$

$= \ \textgreater \ 9^x * 9^2 - 9^x = 240$

$= \ \textgreater \ 9^x(9^2 - 1) = 240$

$= \ \textgreater \ 9^x * (81 - 1) = 240$

$= \ \textgreater \ 9^x * 80 = 240$

$= \ \textgreater \ 9^x = \frac{240}{80}$

$= \ \textgreater \ 9^x = 3$

$= \ \textgreater \ 3^2^{x} = 3^1$

$= \ \textgreater \ 2x = 1$

$= \ \textgreater \ x = \frac{1}{2}$



Hope this helps!

Answer 2

${9}^{x + 2} = 240 + {9}^{x} \\ \\ {9}^{x + 2} - {9}^{x} = 240 \\ \\ {9}^{x} ( {9}^{2} - 1) = 240 \\ \\ {9}^{x} (81 - 1) = 240 \\ \\ {9}^{x} \times 80 = 240 \\ \\ {3}^{2x} = 3 \\ \\ {3}^{2x} = {3}^{1} \\ \\ bases \: are \: same \: so \: exponent \: \\ are \: equal \\ \\ 2x = 1 \\ \\ x = \frac{1}{2}$