Question

7D%20" id="TexFormula1" title=" {3}^{x + 2} - {3}^{x} = \frac{8}{9} " alt=" {3}^{x + 2} - {3}^{x} = \frac{8}{9} " align="absmiddle" class="latex-formula">

Answer 1

$3^{x + 2}$ - $3^{x}$ = $3^{x}$* $3^{2}$ - $3^{x}$ = 9($3^{x}$) - 1($3^{x}$) = 8($3^{x}$)

$3^{x + 2}$ - $3^{x}$ = $\frac{8}{9}$

⇒ 8($3^{x}$) = $\frac{8}{9}$

⇒ $3^{x}$ = $\frac{1}{9}$   multiplied both sides by 8

⇒$3^{x}$ = $\frac{1}{3^{2} }$

⇒ $3^{x}$ = 3⁻²

⇒ x = -2

Answer: x = -2