en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 20ln(10)-2ln(10^6)

Solution

simplify

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

Solution

8 ln (10)

+1

Decimal Notation

18.42068 \dots

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

20 ln (10) = ln (1 0^{20})

= ln (1 0^{20}) - 2 ln (1 0^{6})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (1 0^{6}) = ln ((1 0^{6})^{2})

= ln (1 0^{20}) - ln ((1 0^{6})^{2})

Apply log rule:

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

ln (1 0^{20}) - ln ((1 0^{6})^{2}) = ln (\frac{1 0 ^{20}}{( 1 0 ^{6} ) ^{2}})

= ln (\frac{1 0 ^{20}}{( 1 0 ^{6} ) ^{2}})

\frac{1 0 ^{20}}{( 1 0 ^{6} ) ^{2}} = 100000000

= ln (100000000)

Rewrite

100000000

in power-base form:

100000000 = 1 0^{8}

= ln (1 0^{8})

Apply log rule:

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

ln (1 0^{8}) = 8 ln (10)

= 8 ln (10)

Popular Examples

simplify ln((e^3)/9)simplify

ln (\frac{e ^{3}}{9})

simplify log_{2}(3)+log_{2}(6)simplify

lo g_{2} (3) + lo g_{2} (6)

simplify ln((e^7)/(14))simplify

ln (\frac{e ^{7}}{14})

expand log_{10}((y^3\sqrt[3]{z^4})/x)expand

simplify 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z)simplify

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y) - lo g_{3} (z)

Frequently Asked Questions (FAQ)

What is 20*ln(10)-2*ln(10^6) ?
The solution to 20*ln(10)-2*ln(10^6) is 8ln(10)