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Popular >

simplify ln(2e^{x+y})

Solution

simplify

ln (2 e^{x + y})

Solution

ln (2) + x + y

Solution steps

ln (2 e^{x + y})

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{x + y}) = (x + y) ln (e)

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

(x + y) ln (e) = x + y

= ln (2) + x + y

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Frequently Asked Questions (FAQ)

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