Question

if 9 to the power x + 2 is equals to 240 + 9 to the power x find the value of x

Answer 1

$\textbf{ \underline{ Hello Mate! }}$

${9}^{x + 2} = 240 + {9}^{x} \\ {9}^{x} \times {9}^{2} = 240 + {9}^{x} \\ {9}^{x} \times {9}^{2} - {9}^{x} = 240 \\ {9}^{x}( {9}^{2} - 1) = 240 \\ {9}^{x} (81 - 1) = 240 \\ {9}^{x} \times 80 = 240 \\ {9}^{x} = \frac{240}{80} \\ {3}^{2x} = {3}^{1} \\ 2x = 1 = > x = \frac{1}{2}$

Have great future ahead!

Answer 2

Hello!

$\star \: \bf\small{ANSWER}$

$\boxed{\red{\bf{x = \dfrac{1}{2}}}}$

$\star \: \bf\small{EXPLANATION}$ :

$\sf 9^{x+2} = 240+ \sf 9^{x} \\ \\ \implies \sf 9^{x} \times 9^{2} = 240 + \sf 9^{x} \\ \\ \implies \sf 9^{x} \times 9^{2} - 9^{x} = 240 \\ \\ \implies \sf 9^{x}(9^{2}-1) = 240 \\ \\ \implies \sf 9^{x}(81-1) = 240 \\ \\ \implies \sf 9^{x} = \dfrac{240}{80} \implies \sf 3^{2x} = 3^{1}$

Equatin' powers : $\sf 2x = 1 \implies \boxed{\red{\bf{x = \dfrac{1}{2}}}}$

Cheers!