en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x)-ln(x^2)

Solution

simplify

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

Solution

- ln (x)

Solution steps

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

Apply log rule:

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

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

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

Cancel the common factor:

x

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (x)

Popular Examples

simplify ln(8/(3*sqrt(3)))simplify

ln (\frac{8}{3 \cdot 3})

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

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

simplify ln(-4i)simplify

ln (- 4 i)

simplify ln((3^x6^{3x})/(2^{3x)})simplify

ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{3 x}})

simplify log_{10}(4x)+log_{10}(x)simplify

lo g_{10} (4 x) + lo g_{10} (x)

Frequently Asked Questions (FAQ)

What is ln(x)-ln(x^2) ?
The solution to ln(x)-ln(x^2) is -ln(x)