What is rationalize 2ln(7)+ln((pi^6)/3) ?

The solution to rationalize 2ln(7)+ln((pi^6)/3) is 2ln(7)++6ln(pi)-ln(3)

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rationalize 2ln(7)+ln((pi^6)/3)

rationalize

2 ln (7) + ln (\frac{π ^{6}}{3})

2 ln (7) + + 6 ln (π) - ln (3)

Decimal Notation

9.66158 \dots

Solution steps

2 ln (7) + ln (\frac{π ^{6}}{3})

Apply log rule:

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

ln (\frac{π ^{6}}{3}) = ln (π^{6}) - ln (3)

= 2 ln (7) + + ln (π^{6}) - ln (3)

Apply log rule:

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

ln (π^{6}) = 6 ln (π)

= 2 ln (7) + + 6 ln (π) - ln (3)

ln (\frac{x}{x + y})

\frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

5 lo g_{b} (x) + 9 lo g_{b} (y) - 3 lo g_{b} (z)

\frac{25 ( ln ( - 3 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

ln (x^{2} - 1) - ln (x - 1)

What is rationalize 2ln(7)+ln((pi^6)/3) ?
The solution to rationalize 2ln(7)+ln((pi^6)/3) is 2ln(7)++6ln(pi)-ln(3)