Question

How do you fine the inverse of a log function
f(x)=log(3)(x+9)

Answer 1

To find the inverse of the function f(x) = log3(x+9), convert it to its exponential form, switch x and y, and solve for y. The inverse function is f^-1(x) = log3(x). Use the inverse log or exponential calculation on a calculator to find specific values.

Step-by-step explanation:

To find the inverse of the logarithmic function f(x) = log3(x+9), you need to understand the relationship between logarithms and exponentiation. The logarithm function and the exponential function are inverses of each other. Hence, the inverse of f(x) can be found by expressing the equation in its exponential form.

Steps to Find the Inverse Function

1. Start with the original function: f(x) = log3(x+9).
2. Rewrite the function in exponential form to revert the logarithm: 3f(x) = x + 9.
3. Express f(x) as the subject by replacing it with y: 3y = x + 9.
4. To find the inverse function, swap x and y: x = 3y.
5. Rewrite the inverse function, solve for y: y = log3(x).
6. Replace y with f-1(x) to denote the inverse: f-1(x) = log3(x).

You can use your calculator to find specific values by entering the logarithm and taking the inverse log of the number or by calculating 3x where x is the value of the logarithm.

Answer 2

Step-by-step explanation:

`\boxed{inverse\ of\ log_a(b)=a^b}`

Therefore for
`f(x)=log_3(x+9)`

`f^(-1)(x)=3^((x+9))`