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The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator
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$\ln\left(\left(x^2+1\right)^3\right)-\ln\left(2^x\sqrt{x^2+4}\right)$
Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression ln(((x^2+1)^3)/(2^x(x^2+4)^1/2)). 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).