Exercise
$\ln\left(4\right)+\ln\left(4x^2-3\right)=\ln\left(157\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the logarithmic equation ln(4)+ln(4x^2-3)=ln(157). 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. Divide both sides of the equation by 4. We need to isolate the dependent variable x, we can do that by simultaneously subtracting -3 from both sides of the equation.
Solve the logarithmic equation ln(4)+ln(4x^2-3)=ln(157)
Final answer to the exercise
$x=\frac{13}{4},\:x=-\frac{13}{4}$