Solve the logarithmic equation $\log \left(\frac{x\sqrt{x+1}}{x^2-1}\right)=\log \left(x\right)-\frac{1}{2}\log \left(x+1\right)-\log \left(x-1\right)$

Learn how to solve equations problems step by step online. Solve the logarithmic equation log((x*(x+1)^(1/2))/(x^2+-1))=log(x)-1/2log(x+1)-log(x+-1). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Multiply the fraction and term in - \left(-\frac{1}{2}\right)\log \left(x+1\right). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=\frac{1}{2}, b=10 and x=x+1.