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

Question

Solve the equation

x = \frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{5 ln ( π )}

Alternative Form

x \approx 0.20949

Evaluate

\frac{π ^{2} ln ( 2 ^{2} )}{( \frac{x}{l n ( 2 ) - l o g _{π} ( 2 )} ) \times ln ( π )} = 5

Find the domain

More Steps

\frac{π ^{2} ln ( 2 ^{2} )}{( \frac{x}{l n ( 2 ) - l o g _{π} ( 2 )} ) \times ln ( π )} = 5, x \neq = 0

Simplify

More Steps

\frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{ln ( π ) \times x} = 5

Cross multiply

2 (ln (2))^{2} π^{2} - 2 π^{2} lo g_{π} (2) \times ln (2) = ln (π) \times x \times 5

Simplify the equation

2 (ln (2))^{2} π^{2} - 2 π^{2} lo g_{π} (2) \times ln (2) = 5 ln (π) \times x

Swap the sides of the equation

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

Divide both sides

\frac{5 ln ( π ) \times x}{5 ln ( π )} = \frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{5 ln ( π )}

Divide the numbers

x = \frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{5 ln ( π )}

Check if the solution is in the defined range

x = \frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{5 ln ( π )}, x \neq = 0

Solution

x = \frac{2 ( ln ( 2 ) ) ^{2} π ^{2} - 2 π ^{2} lo g _{π} ( 2 ) \times ln ( 2 )}{5 ln ( π )}

Alternative Form

x \approx 0.20949

Show Solution