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Popular >

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

Solution

simplify

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

Solution

ln (x) + y ln (1 - x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

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simplify log_{1.025}(40/13)+4 simplify

lo g_{1.025} (\frac{40}{13}) + 4

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join 1/6 ln(2)join

\frac{1}{6} ln (2)

simplify log_{10}(2pi*501.24*0.98*111.2*10^{-6})simplify

lo g_{10} (2 π \cdot 501.24 \cdot 0.98 \cdot 111.2 \cdot 1 0^{- 6})

Frequently Asked Questions (FAQ)

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