What is ln((e^{2x}cos(3x))/(sqrt(x-4))) ?

The solution to ln((e^{2x}cos(3x))/(sqrt(x-4))) is 2x+ln(cos(3x))-ln(sqrt(x-4))

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simplify ln((e^{2x}cos(3x))/(sqrt(x-4)))

simplify

ln (\frac{e ^{2 x} cos ( 3 x )}{x - 4})

2 x + ln (cos (3 x)) - ln (x - 4)

Solution steps

ln (\frac{e ^{2 x} cos ( 3 x )}{x - 4})

Apply log rule:

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

ln (\frac{e ^{2 x} cos ( 3 x )}{x - 4}) = ln (e^{2 x} cos (3 x)) - ln (x - 4)

= ln (e^{2 x} cos (3 x)) - ln (x - 4)

Apply log rule:

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

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

= ln (e^{2 x}) + ln (cos (3 x)) - ln (x - 4)

Apply log rule:

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

ln (e^{2 x}) = 2 x ln (e)

= 2 x ln (e) + ln (cos (3 x)) - ln (x - 4)

2 x ln (e) = 2 x

= 2 x + ln (cos (3 x)) - ln (x - 4)

\frac{π}{8} ln (\frac{13}{9})

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

- lo g_{2} (\frac{1}{6})

2 lo g_{3} (2) - 3 lo g_{3} (4) + 2 lo g_{3} (5)

2 ln (4) + 2 ln (5)

What is ln((e^{2x}cos(3x))/(sqrt(x-4))) ?
The solution to ln((e^{2x}cos(3x))/(sqrt(x-4))) is 2x+ln(cos(3x))-ln(sqrt(x-4))