6)
Solve for x:
(log(8 x))/(log(3)) = 2
Multiply both sides by log(3):
log(8 x) = 2 log(3)
2 log(3) = log(3^2) = log(9):
log(8 x) = log(9)
Cancel logarithms by taking exp of both sides:
8 x = 9
Divide both sides by 8:
Answer: |x = 9/8
8)
Solve for x:
(2 log(1 - 2 x))/(log(2)) = 12
Divide both sides by 2/(log(2)):
log(1 - 2 x) = 6 log(2)
6 log(2) = log(2^6) = log(64):
log(1 - 2 x) = log(64)
Cancel logarithms by taking exp of both sides:
1 - 2 x = 64
Subtract 1 from both sides:
-2 x = 63
Divide both sides by -2:
Answer: |x = -63/2
9)
Solve for x:
3 log(x) - 7 = 4
Add 7 to both sides:
3 log(x) = 11
Divide both sides by 3:
log(x) = 11/3
Cancel logarithms by taking exp of both sides:
Answer: |x = e^(11/3)
