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Popular >

simplify ln(5*e^{7-x})

Solution

simplify

ln (5 \cdot e^{7 - x})

Solution

ln (5) + 7 - x

Solution steps

ln (5 e^{7 - x})

Apply log rule:

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

ln (5 e^{7 - x}) = ln (5) + ln (e^{7 - x})

= ln (5) + ln (e^{- x + 7})

Apply log rule:

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

ln (e^{7 - x}) = (7 - x) ln (e)

= ln (5) + (7 - x) ln (e)

(7 - x) ln (e) = 7 - x

= ln (5) + 7 - x

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Frequently Asked Questions (FAQ)

What is ln(5*e^{7-x}) ?
The solution to ln(5*e^{7-x}) is ln(5)+7-x