Solve 1/3log_{z}({x^2-1})-log_{z}({y})-4log_{z}({2^2})

$$\frac{ 1 }{ 3 } \log_{ z }({ { x }^{ 2 } -1 }) - \log_{ z }({ y }) -4 \log_{ z }({ { 2 }^{ 2 } })$$

Factor

$$\frac{\ln(x^{2}-1)-3\ln(y)-24\ln(2)}{3\ln(z)}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{\log_{z}\left(x^{2}-1\right)-3\log_{z}\left(y\right)-12\log_{z}\left(4\right)}{3}$$

Consider \ln(x^{2}-1)\times \frac{1}{\ln(z)}-3\ln(y)\times \frac{1}{\ln(z)}-12\ln(2^{2})\times \frac{1}{\ln(z)}. Factor out \frac{1}{\ln(z)}.

$$\frac{\ln(x^{2}-1)-3\ln(y)-24\ln(2)}{\ln(z)}$$

Rewrite the complete factored expression.

$$\frac{\ln(x^{2}-1)-3\ln(y)-24\ln(2)}{3\ln(z)}$$

Evaluate

$$\frac{\ln(x^{2}-1)-3\ln(y)-24\ln(2)}{3\ln(z)}$$