What is 8/pi*ln(6)+2/pi*ln(7/6) ?

The solution to 8/pi*ln(6)+2/pi*ln(7/6) is 2/pi ln(1512)

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simplify 8/piln(6)+2/piln(7/6)

simplify

\frac{8}{π} \cdot ln (6) + \frac{2}{π} \cdot ln (\frac{7}{6})

\frac{2}{π} ln (1512)

Decimal Notation

4.66081 \dots

Solution steps

\frac{8}{π} ln (6) + \frac{2}{π} ln (\frac{7}{6})

Apply log rule:

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

\frac{8}{π} ln (6) = ln (6^{\frac{8}{π}})

= ln (6^{\frac{8}{π}}) + \frac{2}{π} ln (\frac{7}{6})

Apply log rule:

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

\frac{2}{π} ln (\frac{7}{6}) = ln ((\frac{7}{6})^{\frac{2}{π}})

= ln (6^{\frac{8}{π}}) + ln ((\frac{7}{6})^{\frac{2}{π}})

Apply log rule:

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

ln (6^{\frac{8}{π}}) + ln ((\frac{7}{6})^{\frac{2}{π}}) = ln (6^{\frac{8}{π}} (\frac{7}{6})^{\frac{2}{π}})

= ln (6^{\frac{8}{π}} (\frac{7}{6})^{\frac{2}{π}})

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

6^{\frac{8}{π}} (\frac{7}{6})^{\frac{2}{π}} = (6^{4} \cdot \frac{7}{6})^{\frac{2}{π}}

= ln ((6^{4} \cdot \frac{7}{6})^{\frac{2}{π}})

Apply log rule

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

assuming

x \geq 0

= \frac{2}{π} ln (6^{4} \cdot \frac{7}{6})

Multiply

6^{4} \cdot \frac{7}{6} : 1512

= \frac{2}{π} ln (1512)

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What is 8/pi*ln(6)+2/pi*ln(7/6) ?
The solution to 8/pi*ln(6)+2/pi*ln(7/6) is 2/pi ln(1512)