Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(x)+ln(x-7)=ln(8x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \ln(a)=\ln(b) then a must equal b. Cancel x from both sides of the equation. We need to isolate the dependent variable x, we can do that by simultaneously subtracting -7 from both sides of the equation.

Solve the logarithmic equation ln(x)+ln(x-7)=ln(8x)