en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(10)-ln(40)

Solution

simplify

ln (10) - ln (40)

Solution

- 2 ln (2)

+1

Decimal Notation

- 1.38629 \dots

Solution steps

ln (10) - ln (40)

Apply log rule:

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

ln (10) - ln (40) = ln (\frac{10}{40})

= ln (\frac{10}{40})

Cancel the common factor:

10

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

Apply log rule:

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

= - 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

expand log_{10}(x^3y)expand

lo g_{10} (x^{3} y)

simplify ln(x)+ln(25)simplify

ln (x) + ln (25)

simplify ln(y+1)-ln(y-1)simplify

ln (y + 1) - ln (y - 1)

simplify-log_{10}(4.5*10^{-11})simplify

- lo g_{10} (4.5 \cdot 1 0^{- 11})

simplify ln(1/(e^y+1))simplify

ln (\frac{1}{e ^{y} + 1})

Frequently Asked Questions (FAQ)

What is ln(10)-ln(40) ?
The solution to ln(10)-ln(40) is -2ln(2)