What is expand ln(sqrt((2x^3)/y)) ?

The solution to expand ln(sqrt((2x^3)/y)) is 1/2 ln((2x^3)/y)

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expand ln(sqrt((2x^3)/y))

expand

ln (\frac{2 x ^{3}}{y})

\frac{1}{2} ln (\frac{2 x ^{3}}{y})

Solution steps

ln (\frac{2 x ^{3}}{y})

Rewrite as

= ln ((\frac{2 x ^{3}}{y})^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} ln (\frac{2 x ^{3}}{y})

(- \frac{1}{4} x - \frac{3}{2}) - (\frac{3}{2} x + \frac{1}{3})

\frac{e ^{- x} - 2 e ^{- 2 x}}{( x ^{2} ) ( x ^{2} + 4 )}

\frac{( 2 n - 1 ) x ^{2 (n - 1)}}{2 n ( 2 n + 1 )}

\frac{3 ^{n + 2} - ( - 1 ) ^{n}}{4}

cos (t) h (t - π)

What is expand ln(sqrt((2x^3)/y)) ?
The solution to expand ln(sqrt((2x^3)/y)) is 1/2 ln((2x^3)/y)