en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((2*10^6)/(10^6))

Solution

simplify

ln (\frac{2 \cdot 1 0 ^{6}}{1 0 ^{6}})

Solution

ln (2)

+1

Decimal Notation

0.69314 \dots

Solution steps

ln (\frac{2 \cdot 1 0 ^{6}}{1 0 ^{6}})

Apply log rule:

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

ln (\frac{2 \cdot 1 0 ^{6}}{1 0 ^{6}}) = ln (2 \cdot 1 0^{6}) - ln (1 0^{6})

= ln (1 0^{6} \cdot 2) - ln (1 0^{6})

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= ln (2 \cdot 1 0^{6}) - 6 ln (10)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 \cdot 1 0^{6}) = ln (2) + ln (1 0^{6})

= ln (2) + ln (1 0^{6}) - 6 ln (10)

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= ln (2) + 6 ln (10) - 6 ln (10)

Add similar elements:

6 ln (10) - 6 ln (10) = 0

= ln (2)

Popular Examples

simplify-log_{10}(3.9*10^{-8})simplify

- lo g_{10} (3.9 \cdot 1 0^{- 8})

simplify-log_{10}(6*10^{-5})simplify

- lo g_{10} (6 \cdot 1 0^{- 5})

simplify 3log_{5}(x)-2log_{5}(y)simplify

3 lo g_{5} (x) - 2 lo g_{5} (y)

simplify-log_{10}(7.5*10^{-5})simplify

- lo g_{10} (7.5 \cdot 1 0^{- 5})

simplify 35e^6+ln(8/5)+45 simplify

35 e^{6} + ln (\frac{8}{5}) + 45

Frequently Asked Questions (FAQ)

What is ln((2*10^6)/(10^6)) ?
The solution to ln((2*10^6)/(10^6)) is ln(2)