What is ln((-1)/3 e^{9x}) ?

The solution to ln((-1)/3 e^{9x}) is ln(-1)-ln(3)+9x

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simplify ln((-1)/3 e^{9x})

simplify

ln (\frac{- 1}{3} e^{9 x})

ln (- 1) - ln (3) + 9 x

Solution steps

ln (\frac{- 1}{3} e^{9 x})

Apply log rule:

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

ln (\frac{- 1}{3} e^{9 x}) = ln (\frac{- 1}{3}) + ln (e^{9 x})

= ln (\frac{- 1}{3}) + ln (e^{9 x})

Apply log rule:

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

ln (e^{9 x}) = 9 x ln (e)

= ln (\frac{- 1}{3}) + 9 x ln (e)

Apply log rule:

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

ln (\frac{- 1}{3}) = ln (- 1) - ln (3)

= ln (- 1) - ln (3) + 9 ln (e) x

9 x ln (e) = 9 x

= ln (- 1) - ln (3) + 9 x

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What is ln((-1)/3 e^{9x}) ?
The solution to ln((-1)/3 e^{9x}) is ln(-1)-ln(3)+9x