# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

$-\ln\left(x\right)+\ln\left(2x^3\right)=5.0876$

Learn how to solve rational equations problems step by step online. Solve the equation ln((1/x))+ln(2*x^3)=ln(486)-ln(3). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. 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). Simplify the fraction by x. Take the variable outside of the logarithm.

$x=9$
$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$