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Popular >

simplify ln((1-p)^{xi-1}p)

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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Frequently Asked Questions (FAQ)

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