${\left( {3}^{2} \right)}^{x}-7 \times {3}^{x}+10=0$
Use ${\left( {a}^{m} \right)}^{n}={\left( {a}^{n} \right)}^{m}$ to transform the expression${\left( {3}^{x} \right)}^{2}-7 \times {3}^{x}+10=0$
To get an equation that is easier to solve, substitute $t$ for ${3}^{x}$${t}^{2}-7t+10=0$
Solve the equation for $t$$\begin{array} { l }t=2,\\t=5\end{array}$
Substitute back $t={3}^{x}$$\begin{array} { l }{3}^{x}=2,\\{3}^{x}=5\end{array}$
Solve the equation for $x$$\begin{array} { l }x=\log_{ 3 }({ 2 }),\\{3}^{x}=5\end{array}$
Solve the equation for $x$$\begin{array} { l }x=\log_{ 3 }({ 2 }),\\x=\log_{ 3 }({ 5 })\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }x_1=\log_{ 3 }({ 2 }),& x_2=\log_{ 3 }({ 5 })\end{array} \\&\begin{array} { l }x_1\approx0.63093,& x_2\approx1.46497\end{array}\end{align*}$