en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln(1/4)

Solution

simplify

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

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

- 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)

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

Apply log rule:

lo g_{a} (1) = 0

= - (- ln (4) + 0)

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

= - (- ln (4))

Apply rule

- (- a) = a

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

ln (2^{2}) = 2 ln (2)

= 2 ln (2)

Popular Examples

simplify log_{10}(2x^4)+log_{10}(3x^5)simplify

lo g_{10} (2 x^{4}) + lo g_{10} (3 x^{5})

simplify ln(y)+ln(z)simplify

ln (y) + ln (z)

expand log_{10}((sqrt(y))/(4y+8))expand

lo g_{10} (\frac{y}{4 y + 8})

simplify ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)})simplify

ln ((sin (x))^{x})

Frequently Asked Questions (FAQ)

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