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Popular >

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

Solution

simplify

ln (e^{x} \cdot (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)

Popular Examples

simplify 0.78-(0.0592)/2 log_{10}((0.09)/(0.06))simplify

0.78 - \frac{0.0592}{2} lo g_{10} (\frac{0.09}{0.06})

join 1/9 ln(2)join

\frac{1}{9} ln (2)

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5 ln ∣ x + 2 ∣ - 4 ln ∣ x + 3 ∣

simplify-log_{10}(5.35*10^{-4})simplify

- lo g_{10} (5.35 \cdot 1 0^{- 4})

simplify 7089.884206*ln((1000^2)/(4.5*10^8))simplify

7089.884206 \cdot ln (\frac{100 0 ^{2}}{4.5 \cdot 1 0 ^{8}})

Frequently Asked Questions (FAQ)

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