en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(1/4)

Solution

simplify

2 ln (\frac{1}{4})

Solution

- 4 ln (2)

+1

Decimal Notation

- 2.77258 \dots

Solution steps

2 ln (\frac{1}{4})

Apply log rule:

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

ln (\frac{1}{4}) = ln (1) - ln (4)

= 2 (ln (1) - ln (4))

Apply log rule:

lo g_{a} (1) = 0

= 2 (- ln (4) + 0)

0 - ln (4) = - ln (4)

= 2 (- ln (4))

Remove parentheses:

(- a) = - a

= - 2 ln (4)

Simplify

ln (4) : 2 ln (2)

= - 2 \cdot 2 ln (2)

Multiply the numbers:

2 \cdot 2 = 4

= - 4 ln (2)

Popular Examples

simplify ln((3+x)/(3-x))simplify

ln (\frac{3 + x}{3 - x})

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

ln (x + 1) - ln (1 - x)

simplify ln(x+6)+ln(4-2x)simplify

ln (x + 6) + ln (4 - 2 x)

simplify-log_{10}(2.4*10^{-8})simplify

- lo g_{10} (2.4 \cdot 1 0^{- 8})

simplify 3ln(4)+4ln(3)-4ln(3)simplify

3 ln (4) + 4 ln (3) - 4 ln (3)

Frequently Asked Questions (FAQ)

What is 2ln(1/4) ?
The solution to 2ln(1/4) is -4ln(2)