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Popular >

simplify ln(e^{-x}cos^2(x))

Solution

simplify

ln (e^{- x} cos^{2} (x))

Solution

- x + ln (cos^{2} (x))

Solution steps

ln (e^{- x} cos^{2} (x))

Apply log rule:

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

ln (e^{- x} cos^{2} (x)) = ln (e^{- x}) + ln (cos^{2} (x))

= ln (e^{- x}) + ln (cos^{2} (x))

Apply log rule:

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

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

= - x ln (e) + ln (cos^{2} (x))

x ln (e) = x

= - x + ln (cos^{2} (x))

Popular Examples

simplify ln((58)/(66.6))simplify

ln (\frac{58}{66.6})

simplify 5log_{a}(y-2)-3log_{a}(y+8)simplify

5 lo g_{a} (y - 2) - 3 lo g_{a} (y + 8)

simplify ln(x/((x-2)))simplify

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

simplify-log_{10}(1.9*10^{-5})simplify

- lo g_{10} (1.9 \cdot 1 0^{- 5})

simplify ln(2.69*10^{12})simplify

ln (2.69 \cdot 1 0^{12})

Frequently Asked Questions (FAQ)

What is ln(e^{-x}cos^2(x)) ?
The solution to ln(e^{-x}cos^2(x)) is -x+ln(cos^2(x))