en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln(2)-4ln(6)

Solution

simplify

4 ln (2) - 4 ln (6)

Solution

- 4 ln (3)

+1

Decimal Notation

- 4.39444 \dots

Solution steps

4 ln (2) - 4 ln (6)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (2^{4}) - 4 ln (6)

Apply log rule:

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

4 ln (6) = ln (6^{4})

= ln (2^{4}) - ln (6^{4})

Apply log rule:

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

ln (2^{4}) - ln (6^{4}) = ln (\frac{2 ^{4}}{6 ^{4}})

= ln (\frac{2 ^{4}}{6 ^{4}})

\frac{2 ^{4}}{6 ^{4}} = \frac{1}{81}

= ln (\frac{1}{81})

Apply log rule:

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

= - ln (81)

Rewrite

81

in power-base form:

81 = 3^{4}

= - ln (3^{4})

Apply log rule:

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

ln (3^{4}) = 4 ln (3)

= - 4 ln (3)

Popular Examples

simplify 1/3 ln(5+1)-1/3 ln(5-2)simplify

\frac{1}{3} ln (5 + 1) - \frac{1}{3} ln (5 - 2)

simplify ln(3.17*10^{-9})simplify

ln (3.17 \cdot 1 0^{- 9})

simplify log_{2/pi}(2*pi)simplify

lo g_{\frac{2}{π}} (2 \cdot π)

expand log_{10}(z^6y)expand

lo g_{10} (z^{6} y)

simplify ln((168.92^n)/(146.2^n))simplify

ln (\frac{168.9 2 ^{n}}{146. 2 ^{n}})

Frequently Asked Questions (FAQ)

What is 4ln(2)-4ln(6) ?
The solution to 4ln(2)-4ln(6) is -4ln(3)