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Popular >

simplify ln(x^5e^{y-2})

Solution

simplify

ln (x^{5} e^{y - 2})

Solution

5 ln (x) + y - 2

Solution steps

ln (x^{5} e^{y - 2})

Apply log rule:

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

ln (x^{5} e^{y - 2}) = ln (x^{5}) + ln (e^{y - 2})

= ln (x^{5}) + ln (e^{y - 2})

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= 5 ln (x) + ln (e^{y - 2})

Apply log rule:

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

ln (e^{y - 2}) = (y - 2) ln (e)

= 5 ln (x) + (y - 2) ln (e)

(y - 2) ln (e) = y - 2

= 5 ln (x) + y - 2

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Frequently Asked Questions (FAQ)

What is ln(x^5e^{y-2}) ?
The solution to ln(x^5e^{y-2}) is 5ln(x)+y-2