To solve the equation 8^(3x) = 622, we can take the logarithm of both sides with base 8. The logarithm will help us isolate the exponent.
Step 1: Take the logarithm of both sides with base 8.
log8(8^(3x)) = log8(622)
Step 2: Apply the logarithmic property logb(b^a) = a.
3x = log8(622)
Step 3: Divide both sides of the equation by 3.
x = (1/3) * log8(622)
Now we can use a calculator to evaluate the right-hand side of the equation:
x ≈ (1/3) * log8(622) ≈ (1/3) * 3.973 ≈ 1.324
Therefore, the value of x that satisfies the equation 8^(3x) = 622 is approximately 1.324.