Question

Solve the exponential equation 7ˣ = 49 by expressing each side as a power of the same base and then equating exponents.

a) x = 1
b) x = 2
c) x = 3
d) x = 4

Answer 1

To solve the exponential equation 7ˣ = 49, rewrite both sides as powers of the base 7 and equate the exponents. The correct answer is x = 2.

Step-by-step explanation:

To solve the exponential equation 7ˣ = 49, we can express both sides as powers of the base 7. For example, 49 can be written as 7². Therefore, we can rewrite the equation as 7ˣ = 7².

Next, we can equate the exponents by setting 7ˣ equal to 7². Since the bases are the same, the exponents must be equal, so x = 2. Therefore, the correct answer is b) x = 2.