Advanced MathHardExponential equation with a repeated term
Advanced Math practice question
If 4ˣ + 4ˣ = 2⁷, what is the value of x?
Answer: 3
4ˣ + 4ˣ = 2 · 4ˣ = 2 · 2^(2x) = 2^(2x + 1). So 2x + 1 = 7 and x = 3.
Common wrong answers
- If you answered 6
- 6 comes from 2x = 7 − 1 solved as x = 6.
- If you answered 7
- 7 is the exponent on the right, not x.
- If you answered 3.5
- 3.5 comes from 2x = 7, forgetting the factor 2 from adding the two terms.
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?
Not affiliated with the College Board. SAT is a trademark of the College Board.