what is the range of y=log_8 x

Accepted Solution

Hello!The answer is:Range: All the real numbers or (-∞,+∞)Why?To solve the problem, we need to rewrite the variable "x" as "y" and the variable "y" as "x", and then, isolate "y". Then, we need to look if there is any restriction to the resulting value of "y".We are given the function:[tex]y=log_8(x)[/tex]Now, rewriting we have:[tex]x=log_8(y)[/tex]Then, isolating we have:[tex]8^{x} =8^{(log_8(y))}\\\\8^{x}=y[/tex]Therefore, we can see that the resultant function is a quadratic or polynomial function, we need to remember that there is no restriction for this type of functions, it means that the range of the function is equal to the Real numbers where the values of  "x" exist.Hence, the answer is:Range: All the real numbers or (-∞,+∞)Have a nice day!Note: I have attached a picture for better understanding.