What is ln(θ(θ+1)x^{θ-1}(1-x)) ?

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

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simplify ln(θ(θ+1)x^{θ-1}(1-x))

simplify

ln (θ (θ + 1) x^{θ - 1} (1 - x))

ln (θ) + ln (θ + 1) + (θ - 1) ln (x) + ln (1 - x)

Solution steps

ln (θ (θ + 1) x^{θ - 1} (1 - x))

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{θ - 1}) = (θ - 1) ln (x)

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

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

lo g_{10} (\frac{x}{3 y ^{3}})

ln (\frac{1}{2}) + \frac{π}{6}

3 ln (a) + 2 ln (b)

ln (\frac{1 0 ^{7}}{1 0 ^{6}})

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