What is ln(sqrt(3)+2)-ln(1+sqrt(2))-1/2 ln(2) ?

The solution to ln(sqrt(3)+2)-ln(1+sqrt(2))-1/2 ln(2) is ln((2sqrt(3)+4-2sqrt(2)-sqrt(6))/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

ln (\frac{2 3 + 4 - 2 2 - 6}{2})

Decimal Notation

0.08901 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{3 + 2}{1 + 2} = - (3 + 2) (1 - 2)

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{- ( 3 + 2 ) ( 1 - 2 )}{2 ^{\frac{1}{2}}} = - \frac{6 - 2 3 + 2 2 - 4}{2}

= ln (- \frac{6 - 2 3 + 2 2 - 4}{2})

- \frac{6 - 2 3 + 2 2 - 4}{2} = - \frac{- ( 2 3 + 4 - 2 2 - 6 )}{2} = \frac{2 3 + 4 - 2 2 - 6}{2}

= ln (\frac{2 3 + 4 - 2 2 - 6}{2})

ln (1.2 e^{- 3})

ln (x^{2} 1 - x) + ln (x^{2} 1 - x)

2 \cdot (ln (0.663) - ln (0.583))

24 ln (\frac{\frac{10000}{1500}}{2})

, 6 (- \frac{x}{3})^{\frac{1}{2 l n ( e )}}

What is ln(sqrt(3)+2)-ln(1+sqrt(2))-1/2 ln(2) ?
The solution to ln(sqrt(3)+2)-ln(1+sqrt(2))-1/2 ln(2) is ln((2sqrt(3)+4-2sqrt(2)-sqrt(6))/2)