en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(4pi)

Solution

simplify

ln (4 π)

Solution

2 ln (2) + ln (π)

+1

Decimal Notation

2.53102 \dots

Solution steps

ln (4 π)

Apply log rule:

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

ln (4 π) = ln (4) + ln (π)

= ln (4) + ln (π)

ln (4) = 2 ln (2)

= 2 ln (2) + ln (π)

Popular Examples

simplify log_{3}(c)+log_{3}(c+2)simplify

lo g_{3} (c) + lo g_{3} (c + 2)

simplify 1/3 log_{2}(x)+1/2 log_{2}(y)+log_{2}(z)simplify

\frac{1}{3} lo g_{2} (x) + \frac{1}{2} lo g_{2} (y) + lo g_{2} (z)

simplify ln(2)+ln(9)simplify

ln (2) + ln (9)

simplify 3ln(x+4)+9ln(x-4)-5ln(x)simplify

3 ln (x + 4) + 9 ln (x - 4) - 5 ln (x)

simplify log_{4}((sqrt(y))/(5z^2))simplify

lo g_{4} (\frac{y}{5 z ^{2}})

Frequently Asked Questions (FAQ)

What is ln(4pi) ?
The solution to ln(4pi) is 2ln(2)+ln(pi)