Solve (\pi ^(2)⋅ ln (48^(2)))/(((e^(2)/\pi ^(2)/ ln (

Question

Simplify the expression

\frac{110592 π ^{4} l ^{2} n ^{2} - 110592 π ^{4} l ^{2} n o g _{π}}{e ^{2}}

Evaluate

(π^{2} l n \times 4 8^{2}) \div (((e^{2} \div π^{2} \div l nπ) \div (l n \times 48 - l o g_{π} \times 48)) l nπ)

Dividing by a^{n} is the same as multiplying by a^{- n}

\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( ( e ^{2} \div π ^{2} \div l nπ ) \div ( l n \times 48 - l o g _{π} \times 48 ) ) l n}

Divide the terms

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\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( ( \frac{e ^{2}}{π ^{2}} \div l nπ ) \div ( l n \times 48 - l o g _{π} \times 48 ) ) l n}

Use the commutative property to reorder the terms

\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( ( \frac{e ^{2}}{π ^{2}} \div π l n ) \div ( l n \times 48 - l o g _{π} \times 48 ) ) l n}

Divide the terms

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\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( \frac{e ^{2}}{π ^{3} l n} \div ( l n \times 48 - l o g _{π} \times 48 ) ) l n}

Use the commutative property to reorder the terms

\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( \frac{e ^{2}}{π ^{3} l n} \div ( 48 l n - l o g _{π} \times 48 ) ) l n}

Use the commutative property to reorder the terms

\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{( \frac{e ^{2}}{π ^{3} l n} \div ( 48 l n - 48 l o g _{π} ) ) l n}

Divide the terms

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\frac{π ^{2} l n \times 4 8 ^{2} π ^{- 1}}{\frac{e ^{2}}{π ^{3} l n ( 48 l n - 48 l o g _{π} )} \times l n}

Reduce the fraction

\frac{π ^{2} n \times 4 8 ^{2} π ^{- 1}}{\frac{e ^{2}}{π ^{3} l n ( 48 l n - 48 l o g _{π} )} \times n}

Reduce the fraction

\frac{π ^{2} \times 4 8 ^{2} π ^{- 1}}{\frac{e ^{2}}{π ^{3} l n ( 48 l n - 48 l o g _{π} )}}

Multiply

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\frac{2304 π}{\frac{e ^{2}}{π ^{3} l n ( 48 l n - 48 l o g _{π} )}}

Multiply by the reciprocal

2304 π \times \frac{π ^{3} l n ( 48 l n - 48 l o g _{π} )}{e ^{2}}

Multiply the terms

\frac{2304 π \times π ^{3} l n ( 48 l n - 48 l o g _{π} )}{e ^{2}}

Multiply the terms

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\frac{2304 π ^{4} l n ( 48 l n - 48 l o g _{π} )}{e ^{2}}

Solution

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\frac{110592 π ^{4} l ^{2} n ^{2} - 110592 π ^{4} l ^{2} n o g _{π}}{e ^{2}}

Show Solution

l = 0, n = 0, g_{π} = \frac{n}{o}

Evaluate

(π^{2} l n (4 8^{2})) \div (((e^{2} \div π^{2} \div l nπ) \div (l n \times 48 - l o g_{π} \times 48)) l nπ)

To find the excluded values,set the denominators equal to 0

l n = 0 l n \times 48 - l o g_{π} \times 48 = 0 ((e^{2} \div π^{2} \div l nπ) \div (l n \times 48 - l o g_{π} \times 48)) l nπ = 0

Separate the equation into 2 possible cases

l = 0 n = 0 l n \times 48 - l o g_{π} \times 48 = 0 ((e^{2} \div π^{2} \div l nπ) \div (l n \times 48 - l o g_{π} \times 48)) l nπ = 0

Solve the equations

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l = 0 n = 0 g_{π} = \frac{n}{o} l = 0 ((e^{2} \div π^{2} \div l nπ) \div (l n \times 48 - l o g_{π} \times 48)) l nπ = 0

Solve the equations

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l = 0 n = 0 g_{π} = \frac{n}{o} l = 0 false

Solution

l = 0, n = 0, g_{π} = \frac{n}{o}

Show Solution