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The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator
Learn how to solve expanding logarithms problems step by step online.
$\ln\left(\left(x^4-5\right)^2\right)-\ln\left(\left(x^4-5\right)^6\cos\left(x\right)^6\right)$
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression ln(((x^4-5)^2)/(cos(x)^6(x^4-5)^6)). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).