What is 1/3 (log_{4}(x)-log_{4}(y)) ?

The solution to 1/3 (log_{4}(x)-log_{4}(y)) is (log_{4}(x/y))/3

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simplify 1/3 (log_{4}(x)-log_{4}(y))

simplify

\frac{1}{3} (lo g_{4} (x) - lo g_{4} (y))

\frac{lo g _{4} ( \frac{x}{y} )}{3}

Solution steps

\frac{1}{3} (lo g_{4} (x) - lo g_{4} (y))

Apply log rule:

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

lo g_{4} (x) - lo g_{4} (y) = lo g_{4} (\frac{x}{y})

= \frac{1}{3} lo g_{4} (\frac{x}{y})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot lo g _{4} ( \frac{x}{y} )}{3}

Apply rule:

1 \cdot a = a

1 \cdot lo g_{4} (\frac{x}{y}) = lo g_{4} (\frac{x}{y})

= \frac{lo g _{4} ( \frac{x}{y} )}{3}

ln (x e^{- 2 x})

ln (\frac{( 1 + x )}{( 1 - x )})

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lo g_{2} (\frac{4}{x + 4})

6 (lo g_{8} (5) + lo g_{8} (m))

What is 1/3 (log_{4}(x)-log_{4}(y)) ?
The solution to 1/3 (log_{4}(x)-log_{4}(y)) is (log_{4}(x/y))/3