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

The solution to (2+2ln(2)+1/2+ln(3))-(1-2ln(1)+1+ln(2)) is ln(12)-ln(2)+1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

ln (12) - ln (2) + \frac{1}{2}

Decimal Notation

2.29175 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (2^{2}) + ln (3) = ln (2^{2} \cdot 3)

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

2^{2} \cdot 3 = 12

= 2 + ln (12) + \frac{1}{2} - (1 - 2 ln (1) + 1 + ln (2))

- (1 - 2 ln (1) + 1 + ln (2)) = - (ln (2) + 2)

= 2 + ln (12) + \frac{1}{2} - (ln (2) + 2)

Combine the fractions

2 + \frac{1}{2} : \frac{5}{2}

= ln (12) - (ln (2) + 2) + \frac{5}{2}

- (ln (2) + 2) : - ln (2) - 2

= ln (12) - ln (2) - 2 + \frac{5}{2}

Combine the fractions

- 2 + \frac{5}{2} : \frac{1}{2}

= ln (12) - ln (2) + \frac{1}{2}

lo g_{2} (\frac{4 x ^{3}}{x ^{2} - 3 x - 18})

ln (6) + ln (\frac{e ^{(2.48199)}}{3})

(ln (100) - ln (95)) \cdot 100

lo g_{5} (x - 2) + lo g_{5} (x - 6)

What is (2+2ln(2)+1/2+ln(3))-(1-2ln(1)+1+ln(2)) ?
The solution to (2+2ln(2)+1/2+ln(3))-(1-2ln(1)+1+ln(2)) is ln(12)-ln(2)+1/2