en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1/(10^3))

Solution

simplify

ln (\frac{1}{1 0 ^{3}})

Solution

- 3 ln (10)

+1

Decimal Notation

- 6.90775 \dots

Solution steps

ln (\frac{1}{1 0 ^{3}})

Apply log rule:

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

ln (\frac{1}{1 0 ^{3}}) = ln (1) - ln (1 0^{3})

= ln (1) - ln (1 0^{3})

Apply log rule:

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

ln (1 0^{3}) = 3 ln (10)

= ln (1) - 3 ln (10)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 3 ln (10)

0 - 3 ln (10) = - 3 ln (10)

= - 3 ln (10)

Popular Examples

simplify log_{10}(y^9x)simplify

lo g_{10} (y^{9} x)

simplify 6log_{10}(x)-8log_{10}(x+1)simplify

6 lo g_{10} (x) - 8 lo g_{10} (x + 1)

simplify log_{10}(x^2-4)-log_{10}(x-2)simplify

lo g_{10} (x^{2} - 4) - lo g_{10} (x - 2)

expand ln(((x+3))/(xy))expand

ln (\frac{( x + 3 )}{x y})

simplify 1/4+ln(pi/3)simplify

\frac{1}{4} + ln (\frac{π}{3})

Frequently Asked Questions (FAQ)

What is ln(1/(10^3)) ?
The solution to ln(1/(10^3)) is -3ln(10)