What is ln(149e^{2x+11}e^{-y-17}) ?

The solution to ln(149e^{2x+11}e^{-y-17}) is 2x+ln(149)-y-6

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simplify ln(149e^{2x+11}e^{-y-17})

simplify

ln (149 e^{2 x + 11} e^{- y - 17})

2 x + ln (149) - y - 6

Solution steps

ln (149 e^{2 x + 11} e^{- y - 17})

Apply log rule:

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

ln (149 e^{2 x + 11} e^{- y - 17}) = ln (149) + ln (e^{2 x + 11}) + ln (e^{- y - 17})

= ln (149) + ln (e^{2 x + 11}) + ln (e^{- y - 17})

Apply log rule:

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

ln (e^{2 x + 11}) = (2 x + 11) ln (e)

= ln (149) + (2 x + 11) ln (e) + ln (e^{- y - 17})

Apply log rule:

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

ln (e^{- y - 17}) = (- y - 17) ln (e)

= ln (149) + (2 x + 11) ln (e) + (- y - 17) ln (e)

(2 x + 11) ln (e) = 2 x + 11

(- y - 17) ln (e) = - y - 17

= ln (149) + 2 x + 11 + (- y - 17)

Remove parentheses:

(- a) = - a

= ln (149) + 2 x + 11 - y - 17

Group like terms

= 2 x - y + ln (149) + 11 - 17

Add/Subtract the numbers:

11 - 17 = - 6

= 2 x + ln (149) - y - 6

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What is ln(149e^{2x+11}e^{-y-17}) ?
The solution to ln(149e^{2x+11}e^{-y-17}) is 2x+ln(149)-y-6