Final answer:
To solve the exponential inequality 4^2x < 16, we express both sides with the same base and find that x < 1. Thus, the solution set includes all real numbers less than 1.
Step-by-step explanation:
The exponential inequality in question is 42x < 16.
To solve this inequality, we need to express both sides with the same base if possible. Since 16 is 4 squared (42), we can rewrite the inequality as 42x < 42.
Now, since we have the same base, we can drop the bases and set the exponents equal to each other, that is 2x < 2.
Dividing both sides by 2, we find that x < 1. Therefore, the solution set for the inequality is all real numbers less than 1.