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Popular >

simplify ln(e^x(x-1))

Solution

simplify

ln (e^{x} (x - 1))

Solution

x + ln (x - 1)

Solution steps

ln (e^{x} (x - 1))

Apply log rule:

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

ln (e^{x} (x - 1)) = ln (e^{x}) + ln (x - 1)

= ln (e^{x}) + ln (x - 1)

Apply log rule:

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

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

= x ln (e) + ln (x - 1)

x ln (e) = x

= x + ln (x - 1)

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Frequently Asked Questions (FAQ)

What is ln(e^x(x-1)) ?
The solution to ln(e^x(x-1)) is x+ln(x-1)