What is the inverse of the function y=3^x
To find the inverse of a function, you need to interchange the roles of x and y, and solve the resulting equation for y.
In this case, the original function is y = 3^x. Let's interchange x and y to get x = 3^y.
To solve for y, we will take the logarithm of both sides of the equation. Since the base is 3, we will use the logarithm with base 3, denoted as log₃.
log₃(x) = log₃(3^y)
Using the property of logarithms that states logₐ(a^b) = b * logₐ(a), we can rewrite the equation as:
log₃(x) = y * log₃(3)
Since log₃(3) equals 1, the equation simplifies to:
log₃(x) = y
Now, let's express y in terms of x:
y = log₃(x)
Therefore, the inverse of the function y = 3^x is y = log₃(x).