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

The solution to ln(x/(sqrt(x)*y^3)) is ln(x)-ln(sqrt(x))-3ln(y)

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simplify ln(x/(sqrt(x)*y^3))

simplify

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

ln (x) - ln (x) - 3 ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (x) - ln (y^{3} x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x y^{3}) = ln (x) + ln (y^{3})

= ln (x) - (ln (x) + ln (y^{3}))

Apply log rule:

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

ln (y^{3}) = 3 ln (y)

= ln (x) - (ln (x) + 3 ln (y))

- (ln (x) + 3 ln (y)) : - ln (x) - 3 ln (y)

= ln (x) - ln (x) - 3 ln (y)

ln (x^{r}) + ln (y^{r})

3 ln (2 x)

4 ln (\frac{2}{23})

ln (x) - ln (x + 2)

lo g_{10} (10 z)

What is ln(x/(sqrt(x)*y^3)) ?
The solution to ln(x/(sqrt(x)*y^3)) is ln(x)-ln(sqrt(x))-3ln(y)