What is (98pi)/3 (1+3ln(3)-6ln(2)) ?

The solution to (98pi)/3 (1+3ln(3)-6ln(2)) is (98pi)/3 (1+ln(27/64))

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simplify (98pi)/3 (1+3ln(3)-6ln(2))

simplify

\frac{98 π}{3} (1 + 3 ln (3) - 6 ln (2))

\frac{98 π}{3} (1 + ln (\frac{27}{64}))

Decimal Notation

14.05493 \dots

Solution steps

\frac{98 π}{3} (1 + 3 ln (3) - 6 ln (2))

Apply log rule:

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

3 ln (3) = ln (3^{3})

= \frac{98 π}{3} (1 + ln (3^{3}) - 6 ln (2))

Apply log rule:

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

6 ln (2) = ln (2^{6})

= \frac{98 π}{3} (1 + ln (3^{3}) - ln (2^{6}))

Apply log rule:

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

ln (3^{3}) - ln (2^{6}) = ln (\frac{3 ^{3}}{2 ^{6}})

= \frac{98 π}{3} (ln (\frac{3 ^{3}}{2 ^{6}}) + 1)

\frac{3 ^{3}}{2 ^{6}} = \frac{27}{64}

= \frac{98 π}{3} (1 + ln (\frac{27}{64}))

ln (\frac{x}{48})

lo g_{10} (2) + lo g_{10} (0.2)

2 ln (\frac{2 x + 3}{x ^{2} - 3 x + 2})

ln (\frac{x ^{9} x ^{2} + 5}{( x + 5 ) ^{6}})

ln (\frac{0.01}{( 1 - 0.01 )})

What is (98pi)/3 (1+3ln(3)-6ln(2)) ?
The solution to (98pi)/3 (1+3ln(3)-6ln(2)) is (98pi)/3 (1+ln(27/64))