Exercise
$\ln\left(\frac{6y}{5z}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Expand the logarithmic expression ln((6y)/(5z)). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Decompose 6 in it's prime factors.
Expand the logarithmic expression ln((6y)/(5z))
Final answer to the exercise
$\ln\left(2\right)+\ln\left(3\right)+\ln\left(y\right)-\ln\left(5\right)-\ln\left(z\right)$