en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln|x^2+4|-2ln(2)

Solution

simplify

ln x^{2} + 4 - 2 ln (2)

Solution

ln (\frac{x ^{2} + 4}{4})

Solution steps

ln x^{2} + 4 - 2 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln x^{2} + 4 - ln (2^{2})

Apply log rule:

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

ln x^{2} + 4 - ln (2^{2}) = ln (\frac{x ^{2} + 4}{2 ^{2}})

= ln (\frac{x ^{2} + 4}{2 ^{2}})

2^{2} = 4

= ln (\frac{x ^{2} + 4}{4})

Popular Examples

simplify 1/2 ln(y/x)simplify

\frac{1}{2} ln (\frac{y}{x})

expand log_{3}((x^2)/y)expand

lo g_{3} (\frac{x ^{2}}{y})

simplify x-1/2 log_{15}(17)+1/2 log_{15}(3)simplify

x - \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

expand log_{9}((x(x^2+7))/(sqrt(x^2-7)))expand

lo g_{9} (\frac{x ( x ^{2} + 7 )}{x ^{2} - 7})

join 9log_{2sqrt(2)}(2)join

9 lo g_{22} (2)

Frequently Asked Questions (FAQ)

What is ln|x^2+4|-2ln(2) ?
The solution to ln|x^2+4|-2ln(2) is ln((|x^2+4|)/4)