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Popular >

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

Solution

simplify

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

Solution

ln (x) - x + 1

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

= ln (x) - (x - 1)

- (x - 1) : - x + 1

= ln (x) - x + 1

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Frequently Asked Questions (FAQ)

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