Question

Keeping the properties of exponents in mind, to what power must you raise the expression 72 to get 7 as the result?

a) 2

b) 3

c) 4

d) 5

Answer 1

To find the power to which you must raise 72 to get 7 as the result, you need to solve the equation 72^x = 7. By taking the logarithm of both sides, you can find that x is approximately 0.4548.

Step-by-step explanation:

To find the power to which you must raise 72 to get 7 as the result, you need to solve the equation 72x = 7, where x is the power. To solve this equation, you can take the logarithm of both sides. Taking the logarithm base 72 of 7 gives you x. Using the change of base formula, you can find x by using logarithm base 10 and logarithm base 72.

1. Using the change of base formula, x = log72(7) = log10(7) / log10(72)
2. Simplifying, x ≈ 0.8451 / 1.8573 ≈ 0.4548

Therefore, you must raise the expression 72 to the power of approximately 0.4548 to get 7 as the result. This is not one of the given options, so none of the options (a), (b), (c), or (d) are correct.