en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((s^2)/(1+s^2))

Solution

simplify

ln (\frac{s ^{2}}{1 + s ^{2}})

Solution

2 ln (s) - ln (1 + s^{2})

Solution steps

ln (\frac{s ^{2}}{1 + s ^{2}})

Apply log rule:

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

ln (\frac{s ^{2}}{1 + s ^{2}}) = ln (s^{2}) - ln (1 + s^{2})

= ln (s^{2}) - ln (s^{2} + 1)

Apply log rule:

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

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

= 2 ln (s) - ln (1 + s^{2})

Popular Examples

expand log_{9}(((3^3)/7)^4)expand

lo g_{9} ((\frac{3 ^{3}}{7})^{4})

simplify 2ln|ln(x)|+ln(x)simplify

2 ln ∣ ln (x) ∣ + ln (x)

simplify (3/(ln(7)-ln(4)))/(3x+4)simplify

\frac{\frac{3}{l n ( 7 ) - l n ( 4 )}}{3 x + 4}

simplify-log_{10}(7.1*10^{-7})simplify

- lo g_{10} (7.1 \cdot 1 0^{- 7})

simplify 5ln(2)+3ln(x)-1/2 ln(x+9)simplify

5 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 9)

Frequently Asked Questions (FAQ)

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