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Popular >

simplify ln((1-p)^9p^3)

Solution

simplify

ln ((1 - p)^{9} p^{3})

Solution

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

Solution steps

ln ((1 - p)^{9} p^{3})

Apply log rule:

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

ln ((1 - p)^{9} p^{3}) = ln ((1 - p)^{9}) + ln (p^{3})

= ln ((- p + 1)^{9}) + ln (p^{3})

Apply log rule:

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

ln ((1 - p)^{9}) = 9 ln (1 - p)

= 9 ln (1 - p) + ln (p^{3})

Apply log rule:

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

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

= 9 ln (1 - p) + 3 ln (p)

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Frequently Asked Questions (FAQ)

What is ln((1-p)^9p^3) ?
The solution to ln((1-p)^9p^3) is 9ln(1-p)+3ln(p)