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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{- 2}{3}) = ln (- 2) - ln (3)

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

3 x ln (e) = 3 x

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

ln (- \frac{1}{5} e^{- 5 x})

ln (a (x - 3)^{- 1})

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

lo g_{10} (\frac{150}{3.6}) + 1.9

ln (x + 1) - 2 ln (x - 1)

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