Advanced Math practice question

Answer: 3/2 or 1.5

Write both sides with base 3: 9ˣ = (3²)ˣ = 3²ˣ, and 27 = 3³. So 2x = 3 and x = 3/2.

Common wrong answers

If you answered 2

9² = 81, not 27. Check: 9^(3/2) = (√9)³ = 27.

If you answered 3

3 is the exponent on the 27 side (27 = 3³), but the 9 side has exponent 2x, so 2x = 3.

If you answered 18

18 is 27 − 9. This is an equation about exponents; rewrite both sides as powers of 3.

More Advanced Math questions

• Hard
  A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af…
• Hard
  How many real solutions does x² + 4x + 5 = 0 have?
• Hard
  A car worth $20,000 loses 15% of its value each year. What is its value after 2 years?
• Hard
  An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye…
• Hard
  If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))?
• Hard
  The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?