What is ln(373e^{-x+9}e^{2y+14}) ?

The solution to ln(373e^{-x+9}e^{2y+14}) is 2y+23+ln(373)-x

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simplify ln(373e^{-x+9}e^{2y+14})

simplify

ln (373 e^{- x + 9} e^{2 y + 14})

2 y + 23 + ln (373) - x

Solution steps

ln (373 e^{- x + 9} e^{2 y + 14})

Apply log rule:

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

ln (373 e^{- x + 9} e^{2 y + 14}) = ln (373) + ln (e^{- x + 9}) + ln (e^{2 y + 14})

= ln (373) + ln (e^{- x + 9}) + ln (e^{2 y + 14})

Apply log rule:

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

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

= ln (373) + (- x + 9) ln (e) + ln (e^{2 y + 14})

Apply log rule:

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

ln (e^{2 y + 14}) = (2 y + 14) ln (e)

= ln (373) + (- x + 9) ln (e) + (2 y + 14) ln (e)

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

(2 y + 14) ln (e) = 2 y + 14

= ln (373) + (- x + 9) + 2 y + 14

Remove parentheses:

(- a) = - a

= ln (373) - x + 9 + 2 y + 14

Group like terms

= - x + 2 y + ln (373) + 9 + 14

Add the numbers:

9 + 14 = 23

= 2 y + 23 + ln (373) - x

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What is ln(373e^{-x+9}e^{2y+14}) ?
The solution to ln(373e^{-x+9}e^{2y+14}) is 2y+23+ln(373)-x