Question

Type your response in the box. Why do many log functions (those that aren’t transformed in any manner except for a change in the base) have the point (1,0) in common? For example, all of these functions pass through (1,0): f(x) = ln x g(x) = log x h(x) = log2 x

Answer 1

Answer:

The point (1,0) is common to all log functions of the form k(x) = logb x with any base (b). Logarithmic functions share this feature because of a property of exponents that states b0 = 1 for any value of b.

In a log function of the form k(x) = logb x, k(1) = logb 1.

So, by the definition of a logarithm, bk(1) = 1.

Applying the property of exponents to bk(1) = 1 = b0, we get k(1) = 0.

So, (1,0) is a point on the graph.

Step-by-step explanation: