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Popular >

simplify ln(-e^{-x}*x^k)

Solution

simplify

ln (- e^{- x} \cdot x^{k})

Solution

- x + k ln (x)

Solution steps

ln (- e^{- x} x^{k})

Apply log rule:

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

ln (- e^{- x} x^{k}) = ln (e^{- x}) + ln (x^{k})

= ln (e^{- x}) + ln (x^{k})

Apply log rule:

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

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

= - x ln (e) + ln (x^{k})

Apply log rule:

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

ln (x^{k}) = k ln (x)

= - x ln (e) + k ln (x)

x ln (e) = x

= - x + k ln (x)

Popular Examples

simplify log_{2}(1/40)simplify

lo g_{2} (\frac{1}{40})

simplify-log_{10}(7.94*10^{-5})simplify

- lo g_{10} (7.94 \cdot 1 0^{- 5})

simplify ln(1/2)-ln(2)simplify

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

simplify 3log_{10}(x)+log_{10}(y)simplify

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

simplify-log_{10}(2.7*10^{20})simplify

- lo g_{10} (2.7 \cdot 1 0^{20})

Frequently Asked Questions (FAQ)

What is ln(-e^{-x}*x^k) ?
The solution to ln(-e^{-x}*x^k) is -x+kln(x)