What is ln((e^{-3x}cos^2(x))/(x^2+x+1)) ?

The solution to ln((e^{-3x}cos^2(x))/(x^2+x+1)) is -3x+ln(cos^2(x))-ln(x^2+x+1)

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simplify ln((e^{-3x}cos^2(x))/(x^2+x+1))

simplify

ln (\frac{e ^{- 3 x} cos ^{2} ( x )}{x ^{2} + x + 1})

- 3 x + ln (cos^{2} (x)) - ln (x^{2} + x + 1)

Solution steps

ln (\frac{e ^{- 3 x} cos ^{2} ( x )}{x ^{2} + x + 1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e ^{- 3 x} cos ^{2} ( x )}{x ^{2} + x + 1}) = ln (e^{- 3 x} cos^{2} (x)) - ln (x^{2} + x + 1)

= ln (e^{- 3 x} cos^{2} (x)) - ln (x^{2} + x + 1)

Apply log rule:

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

ln (e^{- 3 x} cos^{2} (x)) = ln (e^{- 3 x}) + ln (cos^{2} (x))

= ln (e^{- 3 x}) + ln (cos^{2} (x)) - ln (x^{2} + x + 1)

Apply log rule:

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

ln (e^{- 3 x}) = - 3 x ln (e)

= - 3 x ln (e) + ln (cos^{2} (x)) - ln (x^{2} + x + 1)

3 x ln (e) = 3 x

= - 3 x + ln (cos^{2} (x)) - ln (x^{2} + x + 1)

ln (\frac{2300}{894.25})

lo g_{6} ((\frac{a c}{b ^{5}})^{6})

lo g_{5} (y) - 4 (lo g_{5} (r) + 2 lo g_{5} (t))

lo g_{2} (x) - 7 lo g_{2} (y)

ln (\frac{302.35}{273.15})

What is ln((e^{-3x}cos^2(x))/(x^2+x+1)) ?
The solution to ln((e^{-3x}cos^2(x))/(x^2+x+1)) is -3x+ln(cos^2(x))-ln(x^2+x+1)