What is (-4ln|11|+4ln|-9|)-(-4ln|10|+4ln|-10|) ?

The solution to (-4ln|11|+4ln|-9|)-(-4ln|10|+4ln|-10|) is ln(6561/14641)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-4ln|11|+4ln|-9|)-(-4ln|10|+4ln|-10|)

simplify

(- 4 ln ∣ 11 ∣ + 4 ln ∣ - 9 ∣) - (- 4 ln ∣ 10 ∣ + 4 ln ∣ - 10 ∣)

ln (\frac{6561}{14641})

Decimal Notation

- 0.80268 \dots

Solution steps

(- 4 ln ∣ 11 ∣ + 4 ln ∣ - 9 ∣) - (- 4 ln ∣ 10 ∣ + 4 ln ∣ - 10 ∣)

Apply log rule:

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

4 ln ∣ 11 ∣ = ln (∣ 11 ∣^{4})

= (4 ln ∣ - 9 ∣ - ln (∣ 11 ∣^{4})) - (4 ln ∣ - 10 ∣ - 4 ln ∣ 10 ∣)

Apply log rule:

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

4 ln ∣ - 9 ∣ = ln (∣ - 9 ∣^{4})

= (ln (∣ - 9 ∣^{4}) - ln (∣ 11 ∣^{4})) - (4 ln ∣ - 10 ∣ - 4 ln ∣ 10 ∣)

Apply log rule:

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

ln (∣ - 9 ∣^{4}) - ln (∣ 11 ∣^{4}) = ln (\frac{∣ - 9 ∣ ^{4}}{∣ 11 ∣ ^{4}})

= ln (\frac{∣ - 9 ∣ ^{4}}{∣ 11 ∣ ^{4}}) - (4 ln ∣ - 10 ∣ - 4 ln ∣ 10 ∣)

\frac{∣ - 9 ∣ ^{4}}{∣ 11 ∣ ^{4}} = \frac{6561}{14641}

= ln (\frac{6561}{14641}) - (- 4 ln ∣ 10 ∣ + 4 ln ∣ - 10 ∣)

- (- 4 ln ∣ 10 ∣ + 4 ln ∣ - 10 ∣) = 0

= ln (\frac{6561}{14641}) + 0

ln (\frac{6561}{14641}) + 0 = ln (\frac{6561}{14641})

= ln (\frac{6561}{14641})

lo g_{3} ((x^{2} x^{5})^{3})

ln (1000 e^{- x})

ln (6.472 i)

ln (12) + \frac{1}{2} ln (7) - ln (2)

ln (- 2) - ln (- 5)

What is (-4ln|11|+4ln|-9|)-(-4ln|10|+4ln|-10|) ?
The solution to (-4ln|11|+4ln|-9|)-(-4ln|10|+4ln|-10|) is ln(6561/14641)