What is log_{10}(θ^x(1-θ)^{(1-x)}) ?

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

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simplify log_{10}(θ^x(1-θ)^{(1-x)})

simplify

lo g_{10} (θ^{x} (1 - θ)^{(1 - x)})

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

Solution steps

lo g_{10} (θ^{x} (1 - θ)^{(1 - x)})

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (θ^{x}) = x lo g_{10} (θ)

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

Apply log rule:

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

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

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

lo g_{y} (\frac{x}{8})

ln (\frac{2 x}{y ^{10}})

2 ln (2 + 3) - 2 ln (2 - 3)

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !})

ln (\frac{( l + s )}{s})

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