What is simplify-ln(xy^2) ?

The solution to simplify-ln(xy^2) is -ln(x)-2ln(y)

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simplify-ln(xy^2)

simplify

- ln (x y^{2})

- ln (x) - 2 ln (y)

Solution steps

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

\frac{1}{4} lo g_{10} (2)

- 2 ln (\frac{1}{2})

ln (\frac{e ^{2}}{17})

2 ln (ab c) - 5 ln (a d e)

ln ∣ 5 ∣ - ln ∣ 4 ∣