Solve for x:
(log^3(x+1))/(2 log^3(4)) = 22
(log^3(x+1))/(2 log^3(4)) = (log^3(x+1))/(2 log^3(4)):
(log^3(x+1))/(2 log^3(4)) = 22
Multiply both sides by 2 log^3(4):
log^3(x+1) = 44 log^3(4)
Taking cube roots gives 2^(2/3) 11^(1/3) log(4) times the third roots of unity:
log(x+1) = -((-11)^(1/3) 2^(2/3) log(4)) or log(x+1) = (-2)^(2/3) 11^(1/3) log(4) or log(x+1) = 2^(2/3) 11^(1/3) log(4)
log(x+1) = -(-11)^(1/3) 2^(2/3) log(4) has no solution since True (assuming the principal logarithm):
log(x+1) = (-2)^(2/3) 11^(1/3) log(4) or log(x+1) = 2^(2/3) 11^(1/3) log(4)
log(x+1) = (-2)^(2/3) 11^(1/3) log(4) has no solution since True (assuming the principal logarithm):
log(x+1) = 2^(2/3) 11^(1/3) log(4)
Cancel logarithms by taking exp of both sides:
x+1 = 4^(2^(2/3) 11^(1/3))
Subtract 1 from both sides:
Answer: | x = 4^(2^(2/3) 11^(1/3))-1 =132.50