What is ln(y/(2^y)*(2-x)^{y-1}) ?

The solution to ln(y/(2^y)*(2-x)^{y-1}) is ln(y)-yln(2)+(y-1)ln(2-x)

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simplify ln(y/(2^y)*(2-x)^{y-1})

simplify

ln (\frac{y}{2 ^{y}} \cdot (2 - x)^{y - 1})

ln (y) - y ln (2) + (y - 1) ln (2 - x)

Solution steps

ln (\frac{y}{2 ^{y}} (2 - x)^{y - 1})

Apply log rule:

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

ln (\frac{y}{2 ^{y}} (2 - x)^{y - 1}) = ln (\frac{y}{2 ^{y}}) + ln ((2 - x)^{y - 1})

= ln (\frac{y}{2 ^{y}}) + ln ((- x + 2)^{y - 1})

Apply log rule:

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

ln ((2 - x)^{y - 1}) = (y - 1) ln (2 - x)

= ln (\frac{y}{2 ^{y}}) + (y - 1) ln (2 - x)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{y}{2 ^{y}}) = ln (y) - ln (2^{y})

= ln (y) - ln (2^{y}) + ln (- x + 2) (y - 1)

Apply log rule:

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

ln (2^{y}) = y ln (2)

= ln (y) - y ln (2) + (y - 1) ln (2 - x)

\frac{1}{2} ln (a) + \frac{1}{2} ln (b)

ln (\frac{z + r ^{2} + z ^{2}}{- z + r ^{2} + z ^{2}})

6 ln (4 x)

- ln (\frac{1}{10})

ln (x) - ln (x - 4) - \frac{1}{2} ln (x + 1)

What is ln(y/(2^y)*(2-x)^{y-1}) ?
The solution to ln(y/(2^y)*(2-x)^{y-1}) is ln(y)-yln(2)+(y-1)ln(2-x)