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
+23254 If the problem is: log4 [ (x + 1)3 / 2 ] = 22
Change from log form into exponential form: (x + 1)3 / 2 = 422
Multiply both sides by 2: (x + 1)3 = 2 · 422
Change the form of 422 (x + 1)3 = 2 · ( 2 · 2 )22
(x + 1)3 = 2 · ( 22 )22
(x + 1)3 = 2 · 244
Simplify: (x + 1)3 = 245
Find the cube root of both sides: x + 1 = 215
Subtract 1 from both sides: x = 215 - 1 = 32768 - 1 = 32767
The cube root of 245 is (245)1/3 = 245 x 1/3 = 215.
