Question

For the functions ƒ(x) = log_a(x) and g(x) = log_b(x), for what value(s) of x is ƒ(x) = g(x)?

Answer 1

Change-of-Base Formula :

Let a, b, and x be positive real numbers such that a ≠ 1 and b ≠ 1. Then can be converted to a different base as follows.

The logarithm functions are .

The functions are equal, f(x) = g(x) and solve for x.

.

Changing Bases Using Common Logarithms:

Divide each side by .

      [ log(1) = 0 ]

Apply One - to - One property of logarithm : .

x = 1.

The value of x = 1.