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Popular >

simplify ln(xy^2z^{-4})

Solution

simplify

ln (x y^{2} z^{- 4})

Solution

ln (x) + 2 ln (y) - 4 ln (z)

Solution steps

ln (x y^{2} z^{- 4})

Apply log rule:

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

ln (x y^{2} z^{- 4}) = ln (x) + ln (y^{2}) + ln (z^{- 4})

= ln (x) + ln (y^{2}) + ln (z^{- 4})

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) + ln (z^{- 4})

Apply log rule:

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

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

= ln (x) + 2 ln (y) - 4 ln (z)

Popular Examples

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simplify-ln(100)+ln(101)simplify

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simplify 0.65log_{10}(0.39x)+1.45 simplify

0.65 lo g_{10} (0.39 x) + 1.45

Frequently Asked Questions (FAQ)

What is ln(xy^2z^{-4}) ?
The solution to ln(xy^2z^{-4}) is ln(x)+2ln(y)-4ln(z)