What is expand log_{e}(\sqrt[y]{y/(4-y)}) ?

The solution to expand log_{e}(\sqrt[y]{y/(4-y)}) is (ln(y/(4-y)))/y

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expand log_{e}(\sqrt[y]{y/(4-y)})

expand

\frac{ln ( \frac{y}{4 - y} )}{y}

Solution steps

Apply log rule:

lo g_{e} (x) = ln (x)

Rewrite as

= ln ((\frac{y}{4 - y})^{\frac{1}{y}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{y} ln (\frac{y}{- y + 4})

Multiply fractions:

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

= \frac{1 \cdot ln ( \frac{y}{4 - y} )}{y}

Multiply:

1 \cdot ln (\frac{y}{4 - y}) = ln (\frac{y}{4 - y})

= \frac{ln ( \frac{y}{4 - y} )}{y}

\frac{( 5 - 2 s ^{2} - s ^{3} )}{s ^{2} \cdot ( s - 1 ) ( s - 9 )}

2 (8 + 3)

x (A x + B) cos (x) + x (C x + D) sin (x)

\frac{7 x ( 16 x ^{2} - x ^{3} )}{24}

(1 - cos^{2} (x))^{4}

What is expand log_{e}(\sqrt[y]{y/(4-y)}) ?
The solution to expand log_{e}(\sqrt[y]{y/(4-y)}) is (ln(y/(4-y)))/y