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Popular >

simplify ln(e^{-θn}(θ))

Solution

simplify

ln (e^{- θ n} (θ))

Solution

- n θ + ln (θ)

Solution steps

ln (e^{- θ n} (θ))

Apply log rule:

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

ln (e^{- θ n} (θ)) = ln (e^{- θ n}) + ln (θ)

= ln (e^{- n θ}) + ln (θ)

Apply log rule:

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

ln (e^{- θ n}) = - θ n ln (e)

= - θ n ln (e) + ln (θ)

θ n ln (e) = n θ

= - n θ + ln (θ)

Popular Examples

simplify-log_{10}(1.45*10^{-11})simplify

- lo g_{10} (1.45 \cdot 1 0^{- 11})

expand log_{3}((x/(y^2))^2)expand

lo g_{3} ((\frac{x}{y ^{2}})^{2})

simplify (19.16)/(0.0004*60*0.02)ln(1/(1-0.9))simplify

\frac{19.16}{0.0004 \cdot 60 \cdot 0.02} ln (\frac{1}{1 - 0.9})

simplify ln(x^2+sqrt(1+x^4))-ln(4+sqrt(17))simplify

ln (x^{2} + 1 + x^{4}) - ln (4 + 17)

simplify 1/(-30)ln(7/12)simplify

\frac{1}{- 30} ln (\frac{7}{12})

Frequently Asked Questions (FAQ)

What is ln(e^{-θn}(θ)) ?
The solution to ln(e^{-θn}(θ)) is -nθ+ln(θ)