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Popular >

simplify ln(e^x(ln(x)))

Solution

simplify

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

Solution

x + ln (ln (x))

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

= x + ln (ln (x))

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Frequently Asked Questions (FAQ)

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