What is (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2)) ?

The solution to (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2)) is (9(8ln(2)-ln(0.48pi^2)))/(8pi^2)

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simplify (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2))

simplify

\frac{18}{16 π ^{2}} ln (\frac{( 16 ) ^{2}}{0.03 \cdot 16 π ^{2}})

\frac{9 ( 8 ln ( 2 ) - ln ( 0.48 π ^{2} ) )}{8 π ^{2}}

Decimal Notation

0.45476 \dots

Solution steps

\frac{18}{16 π ^{2}} ln (\frac{( 16 ) ^{2}}{0.03 \cdot 16 π ^{2}})

Apply log rule:

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

ln (\frac{1 6 ^{2}}{0.03 \cdot 16 π ^{2}}) = ln (1 6^{2}) - ln (0.03 \cdot 16 π^{2})

= \frac{18}{16 π ^{2}} (ln (1 6^{2}) - ln (16 \cdot 0.03 π^{2}))

Apply log rule:

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

ln (1 6^{2}) = 2 ln (16)

= \frac{18}{16 π ^{2}} (2 ln (16) - ln (0.03 \cdot 16 π^{2}))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{18 ( 2 ln ( 16 ) - ln ( 0.03 \cdot 16 π ^{2} ) )}{16 π ^{2}}

Multiply the numbers:

0.03 \cdot 16 = 0.48

= \frac{18 ( 2 ln ( 16 ) - ln ( 0.48 π ^{2} ) )}{16 π ^{2}}

Cancel the common factor:

2

= \frac{9 ( 2 ln ( 16 ) - ln ( 0.48 π ^{2} ) )}{8 π ^{2}}

2 ln (16) = 8 ln (2)

= \frac{9 ( 8 ln ( 2 ) - ln ( 0.48 π ^{2} ) )}{8 π ^{2}}

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What is (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2)) ?
The solution to (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2)) is (9(8ln(2)-ln(0.48pi^2)))/(8pi^2)