What is expand ln(e/(xy^2)) ?

The solution to expand ln(e/(xy^2)) is 1-ln(x)-2ln(y)

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expand ln(e/(xy^2))

expand

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

1 - ln (x) - 2 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (e) - (ln (x) + 2 ln (y))

Apply log rule:

lo g_{a} (a) = 1

= 1 - (ln (x) + 2 ln (y))

- (ln (x) + 2 ln (y)) : - ln (x) - 2 ln (y)

= 1 - ln (x) - 2 ln (y)

ln (\frac{37}{38})

ln (2 x) + 2 ln (y) - 5 ln (z)

3 lo g_{10} (x) - lo g_{10} (y)

lo g_{3} ((u^{2} v)^{6})

lo g_{10} (21) - lo g_{10} (7)

What is expand ln(e/(xy^2)) ?
The solution to expand ln(e/(xy^2)) is 1-ln(x)-2ln(y)