Solve for x:
log(x) (2 - log(x)/log(4)) = log(π)
Expand out terms of the left hand side:
2 log(x) - (log^2(x))/log(4) = log(π)
Multiply both sides by -log(4):
log^2(x) - 2 log(4) log(x) = -log(4) log(π)
Add log^2(4) to both sides:
log^2(4) - 2 log(4) log(x) + log^2(x) = log^2(4) - log(4) log(π)
Write the left hand side as a square:
(log(x) - log(4))^2 = log^2(4) - log(4) log(π)
Take the square root of both sides:
log(x) - log(4) = sqrt(log^2(4) - log(4) log(π)) or log(x) - log(4) = -sqrt(log^2(4) - log(4) log(π))
Add log(4) to both sides:
log(x) = log(4) + sqrt(log^2(4) - log(4) log(π)) or log(x) - log(4) = -sqrt(log^2(4) - log(4) log(π))
Cancel logarithms by taking exp of both sides:
x = 4 e^sqrt(log^2(4) - log(4) log(π)) or log(x) - log(4) = -sqrt(log^2(4) - log(4) log(π))
Add log(4) to both sides:
x = 4 e^sqrt(log^2(4) - log(4) log(π)) or log(x) = log(4) - sqrt(log(4)^2 - log(4) log(π))
Cancel logarithms by taking exp of both sides:
x = 4 e^sqrt(log^2(4) - log(4) log(π))= 2.24253438346688
or x = 4 e^(-sqrt(log^2(4) - log(4) log(π)))= 7.13478469626164
2.24253438346688 x 7.13478469626164 = 16