Final answer:
The given equation 4^x+2 = 12 is solved using the change of base formula, resulting in x = log(3) / log(4). The calculated value of x is approximately -0.207519. Option B is the correct answer.
Step-by-step explanation:
To solve the equation 4^x+2 = 12 for x, we first need to isolate the exponential part. We do this by dividing both sides of the equation by 4 so that we have 4^x = 3. Next, we apply the change of base formula for logarithms, which states that log₁ᵗ y = log y / log β.
To find x, we need to take the logarithm of both sides of the equation 4^x = 3. We use:
x = log(3) / log(4)
Upon calculating the values of log(3) and log(4), and performing the division, we find that x is approximately -0.207519, which corresponds to option b. Thus, option b is the correct answer.