Solve the logarithmic equation $1000\left(x+1\right)x^{\log_{x}\left(x+1\right)}=\left(x+1\right)^{\log \left(x+1\right)}$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation 1000(x+1)x^logx(x+1)=(x+1)^log(x+1). Simplifying the logarithm. When multiplying two powers that have the same base (x+1), you can add the exponents. Expand the expression \left(x+1\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Grouping all terms to the left side of the equation.