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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

4.76 + lo g_{10} (\frac{11}{4.8})

ln (x^{2} y)

- lo g_{10} (3646974099 x 1 0^{- 3})

ln (20 x^{3}) - ln (2 x^{0})

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