Expand the logarithmic expression $\ln\left(\frac{\left(4x+3\right)\left(x+2\right)^6}{\left(1-9x\right)^3}\right)$

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$\ln\left(\left(4x+3\right)\left(x+2\right)^6\right)-\ln\left(\left(1-9x\right)^3\right)$

Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression ln(((4x+3)(x+2)^6)/((1-9x)^3)). 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).