Calculate: 7^{-x-8} = 8^{2x}

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Expression: $7^{ - x - 8} = 8^{2x}$

Take the log of both sides of the equation.

$$\ln\left(7^{-x-8}\right)=\ln\left(8^{2x}\right)$$

Expand ln(7-x-8) by moving -x-8 outside the logarithm.

$$\left(-x-8\right)\ln\left(7\right)=\ln\left(8^{2x}\right)$$

Expand ln(82x) by moving 2x outside the logarithm.

$$\left(-x-8\right)\ln\left(7\right)=2x\ln\left(8\right)$$

Solve the equation for x.

$$x=-\frac{8\ln\left(7\right)}{\ln\left(7\right)+2\ln\left(8\right)}$$

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