en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(3)-ln(2)-2ln(2)

Solution

simplify

2 ln (3) - ln (2) - 2 ln (2)

Solution

ln (\frac{9}{8})

+1

Decimal Notation

0.11778 \dots

Solution steps

2 ln (3) - ln (2) - 2 ln (2)

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (3^{2}) - ln (2) - 2 ln (2)

Apply log rule:

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

ln (3^{2}) - ln (2) = ln (\frac{3 ^{2}}{2})

= ln (\frac{3 ^{2}}{2}) - 2 ln (2)

3^{2} = 9

= ln (\frac{9}{2}) - 2 ln (2)

Apply log rule:

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

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

= ln (\frac{9}{2}) - ln (2^{2})

Apply log rule:

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

ln (\frac{9}{2}) - ln (2^{2}) = ln (\frac{\frac{9}{2}}{2 ^{2}})

= ln (\frac{\frac{9}{2}}{2 ^{2}})

\frac{\frac{9}{2}}{2 ^{2}} = \frac{9}{8}

= ln (\frac{9}{8})

Popular Examples

simplify-log_{10}(2*10^{-1})simplify

- lo g_{10} (2 \cdot 1 0^{- 1})

simplify 4log_{5}(x)-3log_{5}(y)simplify

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

simplify 0.026ln(0.095)+0.416ln(10)simplify

0.026 ln (0.095) + 0.416 ln (10)

simplify-ln(1/(sqrt(2)))simplify

- ln (\frac{1}{2})

simplify log_{2}(3)+4log_{2}(x)-2log_{2}(y)simplify

lo g_{2} (3) + 4 lo g_{2} (x) - 2 lo g_{2} (y)

Frequently Asked Questions (FAQ)

What is 2ln(3)-ln(2)-2ln(2) ?
The solution to 2ln(3)-ln(2)-2ln(2) is ln(9/8)