What is 2/3 ln(4)-1/3 ln(7) ?

The solution to 2/3 ln(4)-1/3 ln(7) is ln((2\sqrt[3]{2}*7^{2/3})/7)

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simplify 2/3 ln(4)-1/3 ln(7)

simplify

\frac{2}{3} ln (4) - \frac{1}{3} ln (7)

Decimal Notation

0.27555 \dots

Solution steps

\frac{2}{3} ln (4) - \frac{1}{3} ln (7)

Apply log rule:

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

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

= ln (4^{\frac{2}{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{2}{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{2}{3}}) - ln (7^{\frac{1}{3}}) = ln (\frac{4 ^{\frac{2}{3}}}{7 ^{\frac{1}{3}}})

= ln (\frac{4 ^{\frac{2}{3}}}{7 ^{\frac{1}{3}}})

3 lo g_{10} (x^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

ln (\frac{25}{20})

lo g_{b} (2) + lo g_{b} (3)

- \frac{7}{8} lo g_{2} (\frac{7}{8}) - \frac{1}{8} lo g_{2} (\frac{1}{8})

lo g_{10} (\frac{x}{z ^{5} y ^{3}})

What is 2/3 ln(4)-1/3 ln(7) ?
The solution to 2/3 ln(4)-1/3 ln(7) is ln((2\sqrt[3]{2}*7^{2/3})/7)