Final answer:
To solve the equation 4096^x = 8, both numbers are expressed as powers of 2, resulting in the equation 12x = 3, which simplifies to x = 1/4.
Step-by-step explanation:
To solve for x in the equation 4096^x = 8, we first need to express both numbers as powers of the same base. We recognize that 4096 is a power of 2, specifically 2^12 since 2^12 = 4096. Next, we must express 8 as a power of 2, and since 8 = 2^3, we can now rewrite the original equation as (2^12)^x = 2^3.
Now, since the bases are the same, we can set the exponents equal to each other, leading to the equation 12x = 3. To find the value of x, we divide both sides by 12: x = 3/12, which simplifies to x = 1/4. Therefore, the value of x is 1/4.