Exercise
$\ln\left(\sqrt{\frac{x^2}{x^6+1}}\right)$
Step-by-step Solution
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression ln(((x^2)/(x^6+1))^(1/2)). 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. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Multiply the single term \frac{1}{2} by each term of the polynomial \left(2\ln\left(x\right)-\ln\left(x^6+1\right)\right).
Expand the logarithmic expression ln(((x^2)/(x^6+1))^(1/2))
Final answer to the exercise
$\ln\left(x\right)-\frac{1}{2}\ln\left(x^6+1\right)$