Exercise
$\log\left(3-x\right)-\log\left(x+2\right)=\log\left(x+1\right)$
Step-by-step Solution
Learn how to solve integrals of exponential functions problems step by step online. Solve the logarithmic equation log(3+-1*x)-log(x+2)=log(x+1). 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 \log(a)=\log(b) then a must equal b. Multiply both sides of the equation by x+2. Multiplying polynomials x+1 and x+2.
Solve the logarithmic equation log(3+-1*x)-log(x+2)=log(x+1)
Final answer to the exercise
$x=\frac{-4+\sqrt{20}}{2},\:x=\frac{-4-\sqrt{20}}{2}$