If f(x) = log₃ (x + 1), what is f^-1(2)?

Solution:

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

y = f(x) = log₃ (x + 1)

y = log₃ (x + 1)

3^y = (x + 1)

x = 3^y - 1

Interchange x and y

y = 3^x - 1

f^-1(2) = 3² - 1 = 9 - 1 = 8

If f(x) = log₃ (x + 1), what is f^-1(2)?

Summary:

If f(x) = log₃ (x + 1), f^-1(2) = 8