Exercise
$2\log_a\left(z\right)+4\left(\log_a\left(x\right)-2\log_a\left(w\right)\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Condense the logarithmic expression 2loga(z)+4(loga(x)-2loga(w)). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right). 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). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=4, b=a and x=\frac{x}{w^{2}}.
Condense the logarithmic expression 2loga(z)+4(loga(x)-2loga(w))
Final answer to the exercise
$\log_{a}\left(\frac{x^4z^2}{w^{8}}\right)$