# Calculate: 5 * 8^{4x}=-17 * 8^{2x}+12

## Expression: $5 \times {8}^{4x}=-17 \times {8}^{2x}+12$

Use ${a}^{mn}={\left( {a}^{n} \right)}^{m}$ to transform the expression

$5 \times {\left( {8}^{2x} \right)}^{2}=-17 \times {8}^{2x}+12$

To get an equation that is easier to solve, substitute $t$ for ${8}^{2x}$

$5{t}^{2}=-17t+12$

Solve the equation for $t$

$\begin{array} { l }t=-4,\\t=\frac{ 3 }{ 5 }\end{array}$

Substitute back $t={8}^{2x}$

$\begin{array} { l }{8}^{2x}=-4,\\{8}^{2x}=\frac{ 3 }{ 5 }\end{array}$

Solve the equation for $x$

$\begin{array} { l }x\notin ℝ,\\{8}^{2x}=\frac{ 3 }{ 5 }\end{array}$

Solve the equation for $x$

$\begin{array} { l }x\notin ℝ,\\x=\frac{ \ln\left({\frac{ 3 }{ 5 }}\right) }{ 6\ln\left({2}\right) }\end{array}$

Find the union

\begin{align*}&x=\frac{ \ln\left({\frac{ 3 }{ 5 }}\right) }{ 6\ln\left({2}\right) } \\&x\approx-0.122828\end{align*}

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