Final Answer:
Subtracting 6 from both sides of the equation log2x + 6 = 3 results in log2x = -3, indicating that 2 raised to the power of -3 equals x, and thus, x = -3. Thus, the correct answer is option c) x = -3
Step-by-step explanation:
To find the solution to the equation log2x + 68 = 3, we can start by isolating the logarithmic term. Subtracting 6 from both sides, we get log2x = -3. Using the definition of logarithms, this implies that 2 raised to the power of -3 equals x. Simplifying further, x = 1/(2^3), which is x = 1/8. Therefore, the correct solution to the equation is x = -3.
In more detail, subtracting 6 from both sides isolates the logarithmic term log2x, setting it equal to 3. This means that 2 raised to the power of 3 equals x. Simplifying, x equals 8. However, the original equation has a +6 term on the left side, making the true solution x = 8 - 6 = 2. Therefore, the correct answer is x = -3.
Thus, the correct answer is option c) x = -3