What is log_{10}(o^{xi}(1-o)^{1-xi}) ?

The solution to log_{10}(o^{xi}(1-o)^{1-xi}) is xilog_{10}(o)+(1-xi)log_{10}(1-o)

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simplify log_{10}(o^{xi}(1-o)^{1-xi})

simplify

lo g_{10} (o^{x i} (1 - o)^{1 - x i})

x i lo g_{10} (o) + (1 - x i) lo g_{10} (1 - o)

Solution steps

lo g_{10} (o^{x i} (1 - o)^{1 - x i})

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (o^{x i}) = x i lo g_{10} (o)

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

Apply log rule:

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

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

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

ln (\frac{155}{100})

f (x) = ln (3 x) + ln (2)

ln (\frac{12 x}{4 x})

ln (\frac{1}{\frac{x}{y}})

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

What is log_{10}(o^{xi}(1-o)^{1-xi}) ?
The solution to log_{10}(o^{xi}(1-o)^{1-xi}) is xilog_{10}(o)+(1-xi)log_{10}(1-o)