# Solve the equation by expressing each side as a power of the same base and then equating exponents. Given: 8^{4x}=3.1

Solve the equation by expressing each side as a power of the same base and then equating exponents. Given: ${8}^{4x}=3.1$
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Step 1 Since the right side value is in decimals, we can’t express each side as a power of the same base. Step 2 We can solve the equation using properties of logarithm. ${8}^{4x}=3.1$
$\mathrm{ln}\left({8}^{4x}\right)=\mathrm{ln}\left(3.1\right)$

$x=\frac{\mathrm{ln}\left(3.1\right)}{12\mathrm{ln}\left(2\right)}$