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)

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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}})

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

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

(\frac{1}{- 0.223}) ln (\frac{1}{2})

- 578.2 - 3000 (ln (22501) - ln (32000))

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ln (\frac{60}{10})

- 4 ln ∣ x - 1 ∣ + 6 ln ∣ x ∣ - \frac{1}{x}

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)