Solve (\pi ^(2)⋅ log_(e) (50)^(2))/((x- log_(\pi ) (5

Evaluate

\frac{π ^{2} ln ( 5 0 ^{2} )}{( x - lo g _{π} ( 50 ) ) \times ln ( π )} = 44

Find the domain

More Steps

\frac{π ^{2} ln ( 5 0 ^{2} )}{( x - lo g _{π} ( 50 ) ) \times ln ( π )} = 44, x \neq = lo g_{π} (50)

Simplify

More Steps

\frac{2 π ^{2} ln ( 50 )}{ln ( π ) \times ( x - lo g _{π} ( 50 ) )} = 44

Cross multiply

2 π^{2} ln (50) = ln (π) \times (x - lo g_{π} (50)) \times 44

Simplify the equation

2 π^{2} ln (50) = 44 ln (π) \times (x - lo g_{π} (50))

Rewrite the expression

2 π^{2} ln (50) = 2 \times 22 ln (π) \times (x - lo g_{π} (50))

Evaluate

π^{2} ln (50) = 22 ln (π) \times (x - lo g_{π} (50))

Swap the sides of the equation

22 ln (π) \times (x - lo g_{π} (50)) = π^{2} ln (50)

Divide both sides

\frac{22 ln ( π ) \times ( x - lo g _{π} ( 50 ) )}{22 ln ( π )} = \frac{π ^{2} ln ( 50 )}{22 ln ( π )}

Divide the numbers

x - lo g_{π} (50) = \frac{π ^{2} ln ( 50 )}{22 ln ( π )}

Divide the numbers

x - lo g_{π} (50) = \frac{π ^{2} lo g _{π} ( 50 )}{22}

Move the constant to the right side

x = \frac{π ^{2} lo g _{π} ( 50 )}{22} + lo g_{π} (50)

Simplify

x = \frac{lo g _{π} ( 50 ) \times ( π ^{2} + 22 )}{22}

Multiply the numbers

x = \frac{π ^{2} lo g _{π} ( 50 ) + 22 lo g _{π} ( 50 )}{22}

Check if the solution is in the defined range

x = \frac{π ^{2} lo g _{π} ( 50 ) + 22 lo g _{π} ( 50 )}{22}, x \neq = lo g_{π} (50)

Solution

x = \frac{π ^{2} lo g _{π} ( 50 ) + 22 lo g _{π} ( 50 )}{22}

Alternative Form

x \approx 4.950538

Solve the equation