What is expand ln(sqrt((x^4)/(y^5))) ?

The solution to expand ln(sqrt((x^4)/(y^5))) is 2ln(x)-5/2 ln(y)

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expand ln(sqrt((x^4)/(y^5)))

expand

ln (\frac{x ^{4}}{y ^{5}})

2 ln (x) - \frac{5}{2} ln (y)

Solution steps

ln (\frac{x ^{4}}{y ^{5}})

\frac{x ^{4}}{y ^{5}} = \frac{x ^{2}}{y ^{2} y}

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= ln (x^{2}) - ln (y^{2} y)

Simplify

ln (x^{2}) : 2 ln (x)

ln (y^{2} y) = \frac{5}{2} ln (y)

= 2 ln (x) - \frac{5}{2} ln (y)

(2 - i 3) (2 - i 3)

(a x^{2} + b x + c) (d x^{2} + e x + f)

(1 - sin (x)) (1 + csc (x)) sin (x)

3 e^{- \frac{x}{5}} (x + 5) + 1

What is expand ln(sqrt((x^4)/(y^5))) ?
The solution to expand ln(sqrt((x^4)/(y^5))) is 2ln(x)-5/2 ln(y)