Review question

# When does $9^x - 3^{x+1} = k$ have one or more real solutions? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7384

## Suggestion

The equation $9^x - 3^{x+1} = k$ has one or more real solutions precisely when

1. $k \geq -9/4$,

2. $k > 0$,

3. $k \leq -1$,

4. $k \geq 5/8$.

Maybe we can change variable so that we are working with an equation of a more familiar form? Would the substitution $y = 3^x$ help?