en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1/(2pi))

Solution

simplify

ln (\frac{1}{2 π})

Solution

- (ln (2) + ln (π))

+1

Decimal Notation

- 1.83787 \dots

Solution steps

ln (\frac{1}{2 π})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{2 π}) = ln (1) - ln (2 π)

= ln (1) - ln (2 π)

Apply log rule:

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

ln (2 π) = ln (2) + ln (π)

= ln (1) - (ln (2) + ln (π))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (2) + ln (π))

0 - (ln (2) + ln (π)) = - (ln (2) + ln (π))

= - (ln (2) + ln (π))

Popular Examples

simplify ln((1+sin(x))/(1-sin(x)))simplify

ln (\frac{1 + sin ( x )}{1 - sin ( x )})

simplify ln(1/(cos(x)))simplify

ln (\frac{1}{cos ( x )})

expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4})expand

simplify log_{10}(zx^5)simplify

lo g_{10} (z x^{5})

expand log_{10}((y^5)/z)expand

lo g_{10} (\frac{y ^{5}}{z})

Frequently Asked Questions (FAQ)

What is ln(1/(2pi)) ?
The solution to ln(1/(2pi)) is -(ln(2)+ln(pi))