Final Answer
$x=9$
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Step-by-step Solution
Problem to solve:
$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$
Specify the solving method
1
Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
$\ln\left(2x^3\left(\frac{1}{x}\right)\right)=\ln\left(486\right)-\ln\left(3\right)$
Learn how to solve logarithmic equations problems step by step online.
$\ln\left(2x^3\left(\frac{1}{x}\right)\right)=\ln\left(486\right)-\ln\left(3\right)$
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. Take the variable outside of the logarithm.
Final Answer
$x=9$