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

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

2020-12-03
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. $$\displaystyle{8}^{{{4}{x}}}={3.1}$$
$$\displaystyle{\ln{{\left({8}^{{{4}{x}}}\right)}}}={\ln{{\left({3.1}\right)}}}$$
$$\displaystyle{4}{x}\ {\ln{{\left({8}\right)}}}={\ln{{\left({3.1}\right)}}}$$
$$\displaystyle{x}={\frac{{{\ln{{\left({3.1}\right)}}}}}{{{12}{\ln{{\left({2}\right)}}}}}}$$

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