Question Video: Determining the Solution Set of an Exponential Function Mathematics

The diagram shows the graph of 𝑓(𝑥) = 2^(2𝑥). Use this graph to find the solution set of the equation 2^(2𝑥) − 12 = 4.

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Video Transcript

The diagram shows the graph of 𝑓 of 𝑥 equals two to the power of two 𝑥. Use this graph to find the solution set of the equation two to the power of two 𝑥 minus 12 equals four.

We can see on the graph that we do indeed have this given function, which is an exponential function. So how does this function relate to the given equation two to the power two 𝑥 minus 12 equals four? Well, let’s begin with a little bit of rearranging. If we add 12 to both sides of this equation, we have two to the power two 𝑥 equals 16. Now, in order to solve this equation, we can use the given function. We really want to know for what value of 𝑥 does the output of the function 𝑓 of 𝑥 equal 16. We can check the points on the graph where 𝑦 equals 16.

Alternatively, we can also think of this as drawing the function 𝑓 of 𝑥 equals 16. The point at which these two lines intersect is the solution to two to the power two 𝑥 is equal to 16. We know that this is also the solution to two to the power of two 𝑥 minus 12 equals four. The input or 𝑥-value of this point of intersection is the solution to the equation. So we can give the answer that the solution to two to the power two 𝑥 minus 12 equals four is the set containing two.