Question 1

Find a number x such that 10²^x + 10^x = 30. Round your answer to four decimal places. A) -0.7782 B) -0.6990 C) 0.7782 D) 0.6990

Accepted Answer

To solve the equation 10^(2x) + 10^x = 30, let y = 10^x. Then the equation becomes y^2 + y - 30 = 0. Solving this quadratic equation using the quadratic formula gives y = 5 or y = -6. Since y = 10^x, y must be positive, so y = 5. Therefore, 10^x = 5, and x = log10(5) ≈ 0.6990.

Question 2

Find a formula for the inverse function of the indicated function f. f(x) = 2^x A) B) C) D)

Accepted Answer