14. If 5(2^x) = 40, what is the value of x?
Answer: B
x = 3
To solve the equation 5(2^x) = 40, we can first isolate 2^x by dividing both sides by 5, resulting in 2^x = 8. Recognizing that 8 is equal to 2^3, we find that x must equal 3.
A) 2
This option is incorrect because substituting x = 2 into the equation gives 5(2^2) = 5(4) = 20, which does not equal 40. Thus, 2 is not the value of x that satisfies the equation.
B) 3
This option is correct. By substituting x = 3 into the equation, we have 5(2^3) = 5(8) = 40, which is exactly the original equation. Therefore, x = 3 is indeed the solution.
C) 4
Choosing x = 4 leads to 5(2^4) = 5(16) = 80, which is greater than 40. Hence, this option does not satisfy the equation.
D) 5
If we set x = 5, we find 5(2^5) = 5(32) = 160, which is significantly larger than 40. Therefore, this option is also incorrect.
Conclusion
The correct answer is x = 3, as it is the only value that satisfies the original equation 5(2^x) = 40. All other options fail to meet the requirement of the equation, confirming that only option B is valid.