To solve this equation, we first need to find a common denominator for the fractions on the left side. The least common denominator for 3, 4, and 8 is 24.

So, we can rewrite the equation as:

8/24x + 6/24x + 3/24*x = 34/45

Now, we can combine the fractions:

(8 + 6 + 3)/24x = 34/45
17/24x = 34/45

To isolate x, we can multiply both sides by the reciprocal of 17/24, which is 24/17:

x = (34/45) * (24/17)
x = 4/5

Therefore, the solution to the equation 1/3x + 1/4x + 1/8x = 34/45 is x = 4/5.