What is ln(x^y*(1-x)^{z-y}) ?

The solution to ln(x^y*(1-x)^{z-y}) is yln(x)+(z-y)ln(1-x)

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simplify ln(x^y*(1-x)^{z-y})

simplify

ln (x^{y} \cdot (1 - x)^{z - y})

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

0.0259 \cdot ln (\frac{4.7 \cdot 1 0 ^{17}}{1.15 \cdot 1 0 ^{14}})

ln (40) - ln (4)

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

- 450 ln (\frac{c}{1.75 b})

ln (\frac{1}{x ( x + 1 ) ( x + 2 )})

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