If 5(2^x) = 40, what is the value of x?

Rationale

x = 3.

To solve the equation 5(2^x) = 40, we can isolate 2^x by dividing both sides by 5, leading to 2^x = 8. Recognizing that 8 is equal to 2^3 reveals that x must equal 3.

A (2) YOUR ANSWER

If x were 2, then 2^x would equal 2^2, which is 4. Substituting this back into the original equation gives 5(4) = 20, not 40. Therefore, this choice does not satisfy the equation.

B (3) CORRECT

When x equals 3, 2^x calculates to 2^3, which is 8. Plugging this value into the original equation results in 5(8) = 40, confirming that this choice is correct.

C (4) YOUR ANSWER

With x equal to 4, 2^x becomes 2^4, which equals 16. Inserting this into the equation yields 5(16) = 80, which is also not equal to 40. Thus, this option is incorrect.

D (5) YOUR ANSWER

If x were 5, then 2^x calculates to 2^5, which is 32. Substituting this value gives 5(32) = 160, far exceeding 40. Therefore, this choice is not valid.

Conclusion

The equation 5(2^x) = 40 simplifies to 2^x = 8, leading to the conclusion that x must equal 3. This establishes option B as the only correct answer, as all other choices yield results that do not satisfy the original equation. Understanding how to manipulate exponential equations is crucial in solving similar mathematical problems.

If 5(2^x) = 40, what is the value of x?

x = 3.

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