Exercise
$\log_b\left(\frac{x^3y^2}{\sqrt{w}}\right)$
Step-by-step Solution
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression logb((x^3*y^2)/(w^(1/2))). 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). Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x^3 and N=y^2. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).
Expand the logarithmic expression logb((x^3*y^2)/(w^(1/2)))
Final answer to the exercise
$3\log_{b}\left(x\right)+2\log_{b}\left(y\right)-\frac{1}{2}\log_{b}\left(w\right)$