What is pi(3*ln(3)-2*ln(2)+1) ?

The solution to pi(3*ln(3)-2*ln(2)+1) is pi(ln(27/4)+1)

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simplify pi(3ln(3)-2ln(2)+1)

simplify

π (3 \cdot ln (3) - 2 \cdot ln (2) + 1)

π (ln (\frac{27}{4}) + 1)

Decimal Notation

9.14059 \dots

Solution steps

π (3 ln (3) - 2 ln (2) + 1)

Apply log rule:

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

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

= π (1 + ln (3^{3}) - 2 ln (2))

Apply log rule:

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

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

= π (1 + ln (3^{3}) - ln (2^{2}))

Apply log rule:

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

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

= π (ln (\frac{3 ^{3}}{2 ^{2}}) + 1)

\frac{3 ^{3}}{2 ^{2}} = \frac{27}{4}

= π (ln (\frac{27}{4}) + 1)

8 lo g_{6} (u) + 9 lo g_{6} (v)

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

lo g_{10} (\frac{y}{z ^{9}})

2 x (ln (x) + ln (2)) - 2 x + e

ln (a t e^{c t})

What is pi(3*ln(3)-2*ln(2)+1) ?
The solution to pi(3*ln(3)-2*ln(2)+1) is pi(ln(27/4)+1)