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Popular >

simplify ln(-1/(x^2)e^x)

Solution

simplify

ln (- \frac{1}{x ^{2}} e^{x})

Solution

x - 2 ln (x)

Solution steps

ln (- \frac{1}{x ^{2}} e^{x})

Apply log rule:

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

ln (- \frac{1}{x ^{2}} e^{x}) = ln (\frac{1}{x ^{2}}) + ln (e^{x})

= ln (\frac{1}{x ^{2}}) + ln (e^{x})

Apply log rule:

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

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

= ln (\frac{1}{x ^{2}}) + x ln (e)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{x ^{2}}) = ln (1) - ln (x^{2})

= ln (1) - ln (x^{2}) + ln (e) x

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= ln (1) - 2 ln (x) + x ln (e)

ln (1) = 0

x ln (e) = x

= 0 - 2 ln (x) + x

0 - 2 ln (x) + x = - 2 ln (x) + x

= x - 2 ln (x)

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Frequently Asked Questions (FAQ)

What is ln(-1/(x^2)e^x) ?
The solution to ln(-1/(x^2)e^x) is x-2ln(x)