Step-by-step Solution

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

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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.

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

Unlock this full step-by-step solution!

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 same base is equal to the logarithm of the division. Simplify the fraction by x. Take the variable outside of the logarithm.

Final Answer

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

Main topic:

Rational equations

Time to solve it:

~ 0.05 s (SnapXam)