Final answer:
To find the value of x in the equation 8^x = 2, express both sides with the same base (2), leading to the equation 2^(3x) = 2^1 which simplifies to x = 1/3.
Step-by-step explanation:
The student's question is: 8^x = 2. In order to find the value of x, we need to express both sides of the equation with the same base. The number 8 is a power of 2, specifically 8 is 2 cubed, or 2^3. Therefore, we can rewrite the equation as (2^3)^x = 2^1. Since the bases are now the same, we can equate the exponents, which gives us 3x = 1. To solve for x, we simply divide both sides by 3. So, x would be 1/3 or approximately 0.333.