What is ln(p^x(1-p)^{n-x}) ?

The solution to ln(p^x(1-p)^{n-x}) is xln(p)+(n-x)ln(1-p)

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simplify ln(p^x(1-p)^{n-x})

simplify

ln (p^{x} (1 - p)^{n - x})

x ln (p) + (n - x) ln (1 - p)

Solution steps

ln (p^{x} (1 - p)^{n - x})

Apply log rule:

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

ln (p^{x} (1 - p)^{n - x}) = ln (p^{x}) + ln ((1 - p)^{n - x})

= ln (p^{x}) + ln ((- p + 1)^{- x + n})

Apply log rule:

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

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

= x ln (p) + ln ((1 - p)^{n - x})

Apply log rule:

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

ln ((1 - p)^{n - x}) = (n - x) ln (1 - p)

= x ln (p) + (n - x) ln (1 - p)

3.3 (lo g_{10} (1601.01) - lo g_{10} (3))

ln (\frac{e}{3})

lo g_{6} (36 p)

2 lo g_{10} (x) + lo g_{10} (5 x)

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