en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(2)-ln(10)

Solution

simplify

ln (2) - ln (10)

Solution

- ln (5)

+1

Decimal Notation

- 1.60943 \dots

Solution steps

ln (2) - ln (10)

Apply log rule:

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

ln (2) - ln (10) = ln (\frac{2}{10})

= ln (\frac{2}{10})

Cancel the common factor:

2

= ln (\frac{1}{5})

Apply log rule:

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

= - ln (5)

Popular Examples

simplify log_{10}(5/x)simplify

lo g_{10} (\frac{5}{x})

simplify log_{2}((x+y)*z)simplify

lo g_{2} ((x + y) \cdot z)

simplify ln(x^2-9)-ln(x+3)simplify

ln (x^{2} - 9) - ln (x + 3)

simplify log_{a}(x)-1/2 log_{a}(z)simplify

lo g_{a} (x) - \frac{1}{2} lo g_{a} (z)

simplify 4log_{10}(3)-6log_{10}(2)simplify

4 lo g_{10} (3) - 6 lo g_{10} (2)

Frequently Asked Questions (FAQ)

What is ln(2)-ln(10) ?
The solution to ln(2)-ln(10) is -ln(5)