What is log_{4}((x-4)/(y^2\sqrt[5]{z)}) ?

The solution to log_{4}((x-4)/(y^2\sqrt[5]{z)}) is log_{4}(x-4)-log_{2}(y)-log_{4}(\sqrt[5]{z})

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simplify log_{4}((x-4)/(y^2\sqrt[5]{z)})

simplify

Solution steps

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

Simplify

Apply the distributive law:

- (a + b) = - a - b

ln (\frac{9}{5 x ^{5} y})

\frac{ln ( \frac{5}{9} ) + 2 ln ( 13 )}{6 ln ( 13 )}

lo g_{15} (\frac{x}{y})

lo g_{10} (P) - lo g_{10} (Q) - lo g_{10} (R)

ln (\frac{x + 2}{x - 2})

What is log_{4}((x-4)/(y^2\sqrt[5]{z)}) ?
The solution to log_{4}((x-4)/(y^2\sqrt[5]{z)}) is log_{4}(x-4)-log_{2}(y)-log_{4}(\sqrt[5]{z})