Home > Precalculus > Exponential and Logistic Graphs

What is the relationship between #y=3^x# and #y=log_3x#?

Answer 1

They are inverse functions, and we demonstrate that a given function is the inverse of another using the following proof.

If #f(x)# and #f^-1(x)# are inverse functions, then #f(f^-1(x)) = x#.

Let #f(x) = log_3(x)# and #f^-1(x) = 3^x#

#f(f^-1(x)) = log_3(3^x) = xlog_3(3) =(xlog3)/log3 = x#

This demonstrates that the two functions have an inverse relationship.

I hope this is useful!

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Lily Anderson

The relationship between ( y = 3^x ) and ( y = \log_3 x ) is that they are inverse functions of each other. In other words, if you graph both functions on the same set of axes, they will be symmetric about the line ( y = x ). This means that for any value of ( x ), if you evaluate ( y = 3^x ), then evaluate ( y = \log_3 x ) using the result of the first evaluation as the input for the second, you will get back the original value of ( x ). Similarly, if you evaluate ( y = \log_3 x ), then evaluate ( y = 3^x ) using the result of the first evaluation as the input for the second, you will get back the original value of ( x ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.