Advanced Math practice question

Answer: 3

3ᵃ = 27·3ᵇ = 3³·3ᵇ = 3^(b + 3), so a = b + 3 and a − b = 3.

Common wrong answers

If you answered 9

9 is 3², from misreading 27 as 3².

If you answered 27

27 is the ratio of the outputs, not the difference of the inputs.

If you answered -3

−3 has the difference the wrong way round.

More Advanced Math questions

• Very hard
  The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b?
• Very hard
  What is the solution to the equation 6/(x − 2) = 3?
• Very hard
  The polynomial p(x) = x³ − 4x has how many distinct real zeros?
• Very hard
  The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of…
• Very hard
  The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a…
• Very hard
  In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…