Multiple choice

The roots of the equation $3^{2x}-10.3^{x}+9=0$ are

  1. $1, 2$
  2. $0, 2$
  3. $0, 1$
  4. $1, 3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let y = 3^x. The equation becomes y^2 - 10y + 9 = 0, which factors as (y-1)(y-9) = 0. Solving for y gives y = 1 or y = 9, so 3^x = 1 (x=0) or 3^x = 9 (x=2).

AI explanation

Treating 3 to the power of x as a single variable, let y equal 3 to the power of x, which transforms the equation into y squared minus 10y plus 9 equals 0. Factoring the quadratic yields y minus 1 times y minus 9 equals 0, so the values of y are 1 and 9. Substituting back gives 3 to the power of x equals 1 and 3 to the power of x equals 9. Solving these simple exponential equations results in x equals 0 and x equals 2. Thus, the roots of the original equation are 0 and 2.

Keep practicing — related questions