en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(p^x(1-p)^m)

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify 1/3 ln(26/31)simplify

\frac{1}{3} ln (\frac{26}{31})

simplify ln(3x^5)simplify

ln (3 x^{5})

simplify log_{e}(5e^{2x})simplify

lo g_{e} (5 e^{2 x})

simplify ln(1000/753)simplify

ln (\frac{1000}{753})

simplify ln(4.5*10^{-6})simplify

ln (4.5 \cdot 1 0^{- 6})

Frequently Asked Questions (FAQ)

What is ln(p^x(1-p)^m) ?
The solution to ln(p^x(1-p)^m) is xln(p)+mln(1-p)