Question
Solve the equation
Solve for x
Solve for gπ
Solve for n
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x=43375πnl−3375πogπl
Evaluate
(π2ln×302)÷((x÷(ln×30−logπ×30))lnπ)=32
Simplify
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Evaluate
(π2ln×302)÷((x÷(ln×30−logπ×30))lnπ)
Dividing by an is the same as multiplying by a−n
(x÷(ln×30−logπ×30))lnπ2ln×302π−1
Use the commutative property to reorder the terms
(x÷(30ln−logπ×30))lnπ2ln×302π−1
Use the commutative property to reorder the terms
(x÷(30ln−30logπ))lnπ2ln×302π−1
Rewrite the expression
30ln−30logπx×lnπ2ln×302π−1
Reduce the fraction
30ln−30logπx×nπ2n×302π−1
Reduce the fraction
30ln−30logπxπ2×302π−1
Multiply
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Multiply the terms
π2×302π−1
Multiply the terms with the same base by adding their exponents
π2−1×302
Subtract the numbers
π×302
Evaluate the power
π×900
Multiply the numbers
900π
30ln−30logπx900π
Multiply by the reciprocal
900π×x30ln−30logπ
Multiply the terms
x900π(30ln−30logπ)
x900π(30ln−30logπ)=32
Rewrite the expression
x27000πln−27000πlogπ=32
Cross multiply
27000πln−27000πlogπ=x×32
Simplify the equation
27000πln−27000πlogπ=32x
Rewrite the expression
8(3375πnl−3375πogπl)=8×4x
Evaluate
3375πnl−3375πogπl=4x
Swap the sides of the equation
4x=3375πnl−3375πogπl
Divide both sides
44x=43375πnl−3375πogπl
Solution
x=43375πnl−3375πogπl
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