What is ln(20)+2ln(1/2)+1/3 ln(27) ?

The solution to ln(20)+2ln(1/2)+1/3 ln(27) is ln(15)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(20)+2ln(1/2)+1/3 ln(27)

simplify

ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)

ln (15)

Decimal Notation

2.70805 \dots

Solution steps

ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)

Apply log rule:

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

2 ln (\frac{1}{2}) = ln ((\frac{1}{2})^{2})

= ln (20) + ln ((\frac{1}{2})^{2}) + \frac{1}{3} ln (27)

Apply log rule:

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

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

= ln (20 (\frac{1}{2})^{2}) + \frac{1}{3} ln (27)

20 (\frac{1}{2})^{2} = 5

= ln (5) + \frac{1}{3} ln (27)

Apply log rule:

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

\frac{1}{3} ln (27) = ln (2 7^{\frac{1}{3}})

= ln (5) + ln (2 7^{\frac{1}{3}})

Apply log rule:

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

ln (5) + ln (2 7^{\frac{1}{3}}) = ln (5 \cdot 2 7^{\frac{1}{3}})

= ln (5 \cdot 2 7^{\frac{1}{3}})

5 \cdot 2 7^{\frac{1}{3}} = 15

= ln (15)

3.3 ln (6) - 7.2 ln (2) - 0.9 ln (2)

ln (\frac{e ^{x} + 2}{e ^{x} - 2})

- 3 ln (x) - 3 ln (y) + 3 ln (z)

\frac{1}{3} ln (8) - ln (x) + 2 ln (x) y

- lo g_{10} (4.2 \cdot 1 0^{- 10})

What is ln(20)+2ln(1/2)+1/3 ln(27) ?
The solution to ln(20)+2ln(1/2)+1/3 ln(27) is ln(15)