What is ln(x^{a-1}(1-x)^{b-1}) ?

The solution to ln(x^{a-1}(1-x)^{b-1}) is (a-1)ln(x)+(b-1)ln(1-x)

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simplify ln(x^{a-1}(1-x)^{b-1})

simplify

ln (x^{a - 1} (1 - x)^{b - 1})

(a - 1) ln (x) + (b - 1) ln (1 - x)

Solution steps

ln (x^{a - 1} (1 - x)^{b - 1})

Apply log rule:

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

ln (x^{a - 1} (1 - x)^{b - 1}) = ln (x^{a - 1}) + ln ((1 - x)^{b - 1})

= ln (x^{a - 1}) + ln ((- x + 1)^{b - 1})

Apply log rule:

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

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

= (a - 1) ln (x) + ln ((1 - x)^{b - 1})

Apply log rule:

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

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

= (a - 1) ln (x) + (b - 1) ln (1 - x)

ln (v x^{5})

2000 ln (\frac{140000}{140000 - 2100 x}) - 9.8 x

2 ln (x) + ln (x + 2)

\frac{1}{2} lo g_{7} (m) + \frac{1}{3} lo g_{7} (y)

ln (\frac{9}{x ^{2} + 2})

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