By inspection, we can observe that the base of both sides of the equation is 7. Therefore, we can equate their exponents:
⟹ x^2 = 7^8
Since both sides of the equation have the same base, the exponents must also be equal:
⟹ x^2 = 8
Taking the square root of both sides, we find:
⟹ x = ±√8
Simplifying the square root of 8, we have:
⟹ x = ±√(4 × 2)
⟹ x = ±√4 × √2
⟹ x = ±2 × √2
The two real solutions are ±2√2.
Since we are asked to enter the lesser solution first, the correct response is:
x = -2√2, 2√2.
Solve x^2=7^8 by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses.
1 answer