What is simplify-(-1/3 ln(5+1)+1/3 ln(5-2)) ?

The solution to simplify-(-1/3 ln(5+1)+1/3 ln(5-2)) is -ln((2^{2/3})/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-(-1/3 ln(5+1)+1/3 ln(5-2))

simplify

- (- \frac{1}{3} ln (5 + 1) + \frac{1}{3} ln (5 - 2))

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

Decimal Notation

0.23104 \dots

Solution steps

- (- \frac{1}{3} ln (5 + 1) + \frac{1}{3} ln (5 - 2))

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

Remove parentheses:

(a) = a

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

ln (\frac{y}{2})

lo g_{10} (\frac{1}{4 \cdot 1 0 ^{- 10}})

ln (\frac{y ^{3} \cdot x ^{2} \cdot y ^{2}}{x ^{(\frac{1}{3})}})

\frac{1}{3} ln ∣ x - 3 ∣ + \frac{1}{3} ln x^{2} + 9

ln (2) ln (\frac{2 y}{0.5})

What is simplify-(-1/3 ln(5+1)+1/3 ln(5-2)) ?
The solution to simplify-(-1/3 ln(5+1)+1/3 ln(5-2)) is -ln((2^{2/3})/2)