What is ln(cos(4x)(e^{-x}(x+5))/x) ?

The solution to ln(cos(4x)(e^{-x}(x+5))/x) is ln(cos(4x))-x+ln(x+5)-ln(x)

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simplify ln(cos(4x)(e^{-x}(x+5))/x)

simplify

ln (cos (4 x) \frac{e ^{- x} ( x + 5 )}{x})

ln (cos (4 x)) - x + ln (x + 5) - ln (x)

Solution steps

ln (cos (4 x) \frac{e ^{- x} ( x + 5 )}{x})

Apply log rule:

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

ln (cos (4 x) \frac{e ^{- x} ( x + 5 )}{x}) = ln (cos (4 x)) + ln (\frac{e ^{- x} ( x + 5 )}{x})

= ln (cos (4 x)) + ln (\frac{e ^{- x} ( x + 5 )}{x})

Apply log rule:

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

ln (\frac{e ^{- x} ( x + 5 )}{x}) = ln (e^{- x} (x + 5)) - ln (x)

= ln (cos (4 x)) + + ln (e^{- x} (x + 5)) - ln (x)

Apply log rule:

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

ln (e^{- x} (x + 5)) = ln (e^{- x}) + ln (x + 5)

= ln (cos (4 x)) + + ln (e^{- x}) + ln (x + 5) - ln (x)

Apply log rule:

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

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

= ln (cos (4 x)) - x ln (e) + ln (x + 5) - ln (x)

x ln (e) = x

= ln (cos (4 x)) - x + ln (x + 5) - ln (x)

ln (e^{k x} sin (2 x))

86.25 + 10 lo g_{10} (\frac{420}{8})

ln (z^{6} (z + 7) 6 (z - 7) 3)

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}})

- lo g_{10} (1.34 \cdot 1 0^{- 11})

What is ln(cos(4x)(e^{-x}(x+5))/x) ?
The solution to ln(cos(4x)(e^{-x}(x+5))/x) is ln(cos(4x))-x+ln(x+5)-ln(x)