What is join (5sqrt(3)pi)/6-(5pi)/4+(5ln(2))/2 ?

The solution to join (5sqrt(3)pi)/6-(5pi)/4+(5ln(2))/2 is (5sqrt(3)pi)/6-(5pi)/4+(ln(32))/2

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join (5sqrt(3)pi)/6-(5pi)/4+(5ln(2))/2

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\frac{5 3 π}{6} - \frac{5 π}{4} + \frac{5 ln ( 2 )}{2}

\frac{5 3 π}{6} - \frac{5 π}{4} + \frac{ln ( 32 )}{2}

Decimal Notation

2.34037 \dots

Solution steps

\frac{5 3 π}{6} - \frac{5 π}{4} + \frac{5 ln ( 2 )}{2}

Apply log rule:

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

5 ln (2) = ln (2^{5})

= \frac{5 3 π}{6} - \frac{5 π}{4} + \frac{ln ( 2 ^{5} )}{2}

2^{5} = 32

= \frac{5 3 π}{6} - \frac{5 π}{4} + \frac{ln ( 32 )}{2}

4 ln (3) - 4 ln (x)

ln (2120) - ln (40)

\frac{3}{2} ln (x + 4) - 3 ln (x) - lo g_{e} (6)

- \frac{1}{4} lo g_{e} (\frac{1}{4}) - \frac{3}{4} lo g_{e} (\frac{3}{4})

- ln (\frac{10 \cdot e ^{- x} + 40 - 4}{10})

What is join (5sqrt(3)pi)/6-(5pi)/4+(5ln(2))/2 ?
The solution to join (5sqrt(3)pi)/6-(5pi)/4+(5ln(2))/2 is (5sqrt(3)pi)/6-(5pi)/4+(ln(32))/2