Learn how to solve problems step by step online. Solve the logarithmic equation ln(x-31)-ln(4-3x)=5ln(2). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). 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). 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. Multiply both sides of the equation by 4-3x.

Solve the logarithmic equation ln(x-31)-ln(4-3x)=5ln(2)