What is 4ln(1)-3ln(2)-4ln(1/2)-3ln(1/2+1) ?

The solution to 4ln(1)-3ln(2)-4ln(1/2)-3ln(1/2+1) is -ln(27/16)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln(1)-3ln(2)-4ln(1/2)-3ln(1/2+1)

simplify

4 ln (1) - 3 ln (2) - 4 ln (\frac{1}{2}) - 3 ln (\frac{1}{2} + 1)

- ln (\frac{27}{16})

Decimal Notation

- 0.52324 \dots

Solution steps

4 ln (1) - 3 ln (2) - 4 ln (\frac{1}{2}) - 3 ln (\frac{1}{2} + 1)

Apply log rule:

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

4 ln (\frac{1}{2}) = ln ((\frac{1}{2})^{4})

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

Apply log rule:

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

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

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

Rewrite

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

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

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

Apply log rule:

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

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

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

(\frac{1}{2})^{4} (\frac{1}{2} + 1)^{3} = \frac{27}{128}

= 4 ln (1) - 3 ln (2) - ln (\frac{27}{128})

Apply log rule:

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

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

= 4 ln (1) - ln (2^{3}) - ln (\frac{27}{128})

Rewrite

- ln (2^{3}) - ln (\frac{27}{128})

- (ln (2^{3}) + ln (\frac{27}{128}))

= 4 ln (1) - (ln (2^{3}) + ln (\frac{27}{128}))

Apply log rule:

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

ln (2^{3}) + ln (\frac{27}{128}) = ln (2^{3} \cdot \frac{27}{128})

= 4 ln (1) - ln (2^{3} \cdot \frac{27}{128})

2^{3} \cdot \frac{27}{128} = \frac{27}{16}

= 4 ln (1) - ln (\frac{27}{16})

4 ln (1) = 0

= 0 - ln (\frac{27}{16})

0 - ln (\frac{27}{16}) = - ln (\frac{27}{16})

= - ln (\frac{27}{16})

ln (\frac{25}{36})

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

lo g_{8} (\frac{1}{625})

ln (\frac{9.96087}{0.46087})

ln (- 1.2 \cdot 1 0^{4})

What is 4ln(1)-3ln(2)-4ln(1/2)-3ln(1/2+1) ?
The solution to 4ln(1)-3ln(2)-4ln(1/2)-3ln(1/2+1) is -ln(27/16)