Advanced MathHardInput where a doubled argument multiplies an exponential by 8
Advanced Math practice question
The function g is defined by g(x) = 2ˣ. For what value of x is g(2x) = 8 · g(x)?
Answer: 3
g(2x) = 2^(2x) and 8 · g(x) = 2³ · 2ˣ = 2^(x + 3). So 2x = x + 3 and x = 3.
Common wrong answers
- If you answered 4
- 4 comes from 2x = x + 4, writing 8 as 2⁴ instead of 2³.
- If you answered 8
- 8 is the multiplier, not x.
- If you answered 1.5
- 1.5 comes from 2x = 3, dropping the x on the right.
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.