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** Step-by-step Solution **

Problem to solve:

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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

Learn how to solve logarithmic equations problems step by step online.

$\ln\left(2\left(\frac{1}{x}\right)x^3\right)=\ln\left(486\right)-\ln\left(3\right)$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(1/x)+ln(2x^3)=ln(486)-ln(3). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Multiply the fraction and term. Simplify the fraction \frac{2x^3}{x} by x. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right).

** Final Answer

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