What is 1/3 ln(4)-1/3 ln(7) ?

The solution to 1/3 ln(4)-1/3 ln(7) is 1/3 ln(4/7)

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simplify 1/3 ln(4)-1/3 ln(7)

simplify

\frac{1}{3} ln (4) - \frac{1}{3} ln (7)

\frac{1}{3} ln (\frac{4}{7})

Decimal Notation

- 0.18653 \dots

Solution steps

\frac{1}{3} ln (4) - \frac{1}{3} ln (7)

Apply log rule:

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

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

= ln (4^{\frac{1}{3}}) - \frac{1}{3} ln (7)

Apply log rule:

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

\frac{1}{3} ln (7) = ln (7^{\frac{1}{3}})

= ln (4^{\frac{1}{3}}) - ln (7^{\frac{1}{3}})

Apply log rule:

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

ln (4^{\frac{1}{3}}) - ln (7^{\frac{1}{3}}) = ln (\frac{4 ^{\frac{1}{3}}}{7 ^{\frac{1}{3}}})

= ln (\frac{4 ^{\frac{1}{3}}}{7 ^{\frac{1}{3}}})

Combine same powers :

Rewrite as

= ln ((\frac{4}{7})^{\frac{1}{3}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{3} ln (\frac{4}{7})

lo g_{3} (8) + lo g_{3} (7)

lo g_{3} (8) + lo g_{3} (5)

lo g_{10} (\frac{2 x}{x + 1})

ln (x e^{- 7 x})

- 9 lo g_{10} (z) + 2 lo g_{10} (x) - 5 lo g_{10} (y)

What is 1/3 ln(4)-1/3 ln(7) ?
The solution to 1/3 ln(4)-1/3 ln(7) is 1/3 ln(4/7)