An exponential equation with a power of on the other side may have solutions that aren't straightforward to find by algebra. Graph each side in Desmos and count where the graphs meet. Check both sides of the -axis: looking only at positive -values can miss a solution.
Hints
- Hint 1
An intersection is a point shared by two graphs. At that point, both sides of the equation have the same value for the same . What would you graph for each side?
- Hint 2
The outputs of are positive even when is negative. Squaring a negative number also gives a positive result, so don't leave negative -values out of your graph.
Step-by-step
Count graph intersections
Step 1Keep negative inputs in view
The exponential function is always positive, including when . For negative , is positive too. So you can't rule out negative solutions before comparing the two sides.
- Step 2
Graph both sides and count
Type and on separate lines. Click where they meet: Desmos shows one point near , plus and . An intersection is a point shared by both graphs. Each intersection gives one real solution because the two sides have the same value there. There are real solutions. Choice C.