What is log_{10}(p^x*(1-p)^{1-x}) ?

The solution to log_{10}(p^x*(1-p)^{1-x}) is xlog_{10}(p)+(1-x)log_{10}(1-p)

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simplify log_{10}(p^x*(1-p)^{1-x})

simplify

lo g_{10} (p^{x} \cdot (1 - p)^{1 - x})

x lo g_{10} (p) + (1 - x) lo g_{10} (1 - p)

Solution steps

lo g_{10} (p^{x} (1 - p)^{1 - x})

Apply log rule:

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

lo g_{10} (p^{x} (1 - p)^{1 - x}) = lo g_{10} (p^{x}) + lo g_{10} ((1 - p)^{1 - x})

= lo g_{10} (p^{x}) + lo g_{10} ((- p + 1)^{- x + 1})

Apply log rule:

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

lo g_{10} (p^{x}) = x lo g_{10} (p)

= x lo g_{10} (p) + lo g_{10} ((1 - p)^{1 - x})

Apply log rule:

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

lo g_{10} ((1 - p)^{1 - x}) = (1 - x) lo g_{10} (1 - p)

= x lo g_{10} (p) + (1 - x) lo g_{10} (1 - p)

ln (x^{2} + 10 x + 24) - ln (x + 6)

ln ((a + b x) e^{4})

ln (4) - ln (33)

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

3.143 + lo g_{10} (\frac{0.667}{0.998})

What is log_{10}(p^x*(1-p)^{1-x}) ?
The solution to log_{10}(p^x*(1-p)^{1-x}) is xlog_{10}(p)+(1-x)log_{10}(1-p)