What is 8/5 ln(4/3)+9/10 ln(81/77) ?

The solution to 8/5 ln(4/3)+9/10 ln(81/77) is ln((4/3)^{8/5}(81/77)^{9/10})

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simplify 8/5 ln(4/3)+9/10 ln(81/77)

simplify

\frac{8}{5} ln (\frac{4}{3}) + \frac{9}{10} ln (\frac{81}{77})

ln ((\frac{4}{3})^{\frac{8}{5}} (\frac{81}{77})^{\frac{9}{10}})

Decimal Notation

0.50587 \dots

Solution steps

\frac{8}{5} ln (\frac{4}{3}) + \frac{9}{10} ln (\frac{81}{77})

Apply log rule:

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

\frac{8}{5} ln (\frac{4}{3}) = ln ((\frac{4}{3})^{\frac{8}{5}})

= ln ((\frac{4}{3})^{\frac{8}{5}}) + \frac{9}{10} ln (\frac{81}{77})

Apply log rule:

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

\frac{9}{10} ln (\frac{81}{77}) = ln ((\frac{81}{77})^{\frac{9}{10}})

= ln ((\frac{4}{3})^{\frac{8}{5}}) + ln ((\frac{81}{77})^{\frac{9}{10}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((\frac{4}{3})^{\frac{8}{5}}) + ln ((\frac{81}{77})^{\frac{9}{10}}) = ln ((\frac{4}{3})^{\frac{8}{5}} (\frac{81}{77})^{\frac{9}{10}})

= ln ((\frac{4}{3})^{\frac{8}{5}} (\frac{81}{77})^{\frac{9}{10}})

0.615 + 0.1 lo g_{10} (\frac{2.19}{2.15})

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

\frac{1}{3} [2 ln (x + 3) + ln (x) - in (x^{2} - 1)]

\frac{2}{3} lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

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

What is 8/5 ln(4/3)+9/10 ln(81/77) ?
The solution to 8/5 ln(4/3)+9/10 ln(81/77) is ln((4/3)^{8/5}(81/77)^{9/10})