The points (0,1)

Question

, (1,14)
, and (2,196)
all lie on the line of the exponential function f(x)=14x
. On which logarithmic function do the points (14,1)
and (196,2)
lie?(1 point)
Responses

g(x)=logx
g left parenthesis x right parenthesis equals logarithm x

g(x)=log14x
g left parenthesis x right parenthesis equals logarithm 14 right parenthesis superscript x baseline

g(x)=log14x
g left parenthesis x right parenthesis equals logarithm subscript 14 baseline x

g(x)=x14
g left parenthesis x right parenthesis equals x superscript 14 baseline

Answer 1

To determine the logarithmic function on which the points (14, 1) and (196, 2) lie, we can start by recalling that logarithmic functions are the inverse of exponential functions.

Given that the function \( f(x) = 14^x \) for the points (0,1), (1,14), and (2,196), we can express the logarithmic function as the inverse of \( f(x) \).

The inverse of \( f(x) \) can be written as:

\[ g(x) = \log_{14}(x) \]

This means that when applying \( g(x) \) to our points:

1. For the point (14, 1): \[ g(14) = \log_{14}(14) = 1 \]

2. For the point (196, 2): \[ g(196) = \log_{14}(196) = 2 \] Since \( 196 = 14^2 \), it follows that \( \log_{14}(196) = 2 \).

Thus, both points (14, 1) and (196, 2) indeed lie on the function \( g(x) = \log_{14}(x) \).

So the correct response is:

g(x) = log₁₄(x)