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Popular >

simplify ln(x^{-4}y^{-3})+3

Solution

simplify

ln (x^{- 4} y^{- 3}) + 3

Solution

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

Solution steps

ln (x^{- 4} y^{- 3}) + 3

Apply log rule:

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

ln (x^{- 4} y^{- 3}) = ln (x^{- 4}) + ln (y^{- 3})

= ln (x^{- 4}) + ln (y^{- 3}) + 3

Apply log rule:

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

ln (x^{- 4}) = - 4 ln (x)

= - 4 ln (x) + ln (y^{- 3}) + 3

Apply log rule:

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

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

= - 4 ln (x) - 3 ln (y) + 3

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Frequently Asked Questions (FAQ)

What is ln(x^{-4}y^{-3})+3 ?
The solution to ln(x^{-4}y^{-3})+3 is -4ln(x)-3ln(y)+3