Solve (\pi ^(2)⋅ ln (30^(2)))/((x/( ln (30)- log_(\pi

Question

Solve the equation

x = \frac{( ln ( 30 ) ) ^{2} π ^{2} - π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{16 ln ( π )}

Alternative Form

x \approx 0.788126

Evaluate

\frac{π ^{2} ln ( 3 0 ^{2} )}{( \frac{x}{l n ( 30 ) - l o g _{π} ( 30 )} ) \times ln ( π )} = 32

Find the domain

More Steps

\frac{π ^{2} ln ( 3 0 ^{2} )}{( \frac{x}{l n ( 30 ) - l o g _{π} ( 30 )} ) \times ln ( π )} = 32, x \neq = 0

Simplify

More Steps

\frac{2 ( ln ( 30 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{ln ( π ) \times x} = 32

Cross multiply

2 (ln (30))^{2} π^{2} - 2 π^{2} lo g_{π} (30) \times ln (30) = ln (π) \times x \times 32

Simplify the equation

2 (ln (30))^{2} π^{2} - 2 π^{2} lo g_{π} (30) \times ln (30) = 32 ln (π) \times x

Rewrite the expression

2 ((ln (30))^{2} π^{2} - π^{2} lo g_{π} (30) \times ln (30)) = 2 \times 16 ln (π) \times x

Evaluate

(ln (30))^{2} π^{2} - π^{2} lo g_{π} (30) \times ln (30) = 16 ln (π) \times x

Swap the sides of the equation

16 ln (π) \times x = (ln (30))^{2} π^{2} - π^{2} lo g_{π} (30) \times ln (30)

Divide both sides

\frac{16 ln ( π ) \times x}{16 ln ( π )} = \frac{( ln ( 30 ) ) ^{2} π ^{2} - π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{16 ln ( π )}

Divide the numbers

x = \frac{( ln ( 30 ) ) ^{2} π ^{2} - π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{16 ln ( π )}

Check if the solution is in the defined range

x = \frac{( ln ( 30 ) ) ^{2} π ^{2} - π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{16 ln ( π )}, x \neq = 0

Solution

x = \frac{( ln ( 30 ) ) ^{2} π ^{2} - π ^{2} lo g _{π} ( 30 ) \times ln ( 30 )}{16 ln ( π )}

Alternative Form

x \approx 0.788126

Show Solution