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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
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$\frac{1}{7}\ln\left(\frac{x^2+1}{x^2-1}\right)$
Learn how to solve problems step by step online. Expand the logarithmic expression ln(((x^2+1)/(x^2-1))^1/7). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Multiply the single term \frac{1}{7} by each term of the polynomial \left(\ln\left(x^2+1\right)-\ln\left(x^2-1\right)\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \frac{1}{7}.