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Popular >

simplify ln(p^3(1-p)^7)

Solution

simplify

ln (p^{3} (1 - p)^{7})

Solution

3 ln (p) + 7 ln (1 - p)

Solution steps

ln (p^{3} (1 - p)^{7})

Apply log rule:

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

ln (p^{3} (1 - p)^{7}) = ln (p^{3}) + ln ((1 - p)^{7})

= ln (p^{3}) + ln ((- p + 1)^{7})

Apply log rule:

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

ln (p^{3}) = 3 ln (p)

= 3 ln (p) + ln ((1 - p)^{7})

Apply log rule:

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

ln ((1 - p)^{7}) = 7 ln (1 - p)

= 3 ln (p) + 7 ln (1 - p)

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Frequently Asked Questions (FAQ)

What is ln(p^3(1-p)^7) ?
The solution to ln(p^3(1-p)^7) is 3ln(p)+7ln(1-p)