quadratic, exponential, and logarithmic functions\nwriting an expression as a single logarithm\nwrite the…

quadratic, exponential, and logarithmic functions\nwriting an expression as a single logarithm\nwrite the expression as a single logarithm.\n$4\\log_{4}(z - 6)-2\\log_{4}(z + 7)$\n$\\log_{\\square}(\\square)$

quadratic, exponential, and logarithmic functions\nwriting an expression as a single logarithm\nwrite the expression as a single logarithm.\n$4\\log_{4}(z - 6)-2\\log_{4}(z + 7)$\n$\\log_{\\square}(\\square)$

Answer

Explanation:

Step1: Apply power rule to logs

$4\log_{4}(z-6) = \log_{4}(z-6)^4$, $2\log_{4}(z+7) = \log_{4}(z+7)^2$

Step2: Rewrite original expression

$\log_{4}(z-6)^4 - \log_{4}(z+7)^2$

Step3: Apply quotient rule to logs

$\log_{4}\left(\frac{(z-6)^4}{(z+7)^2}\right)$

Answer:

$\log_{4}\left(\frac{(z-6)^4}{(z+7)^2}\right)$