Q 5. - Precalculus Enhanced with Graphing Utilities

Question

The graph of every logarithmic function $f\left(x\right)={\log }_a\left(x\right)$where $a>0$, and $a\ne 1$, passes through three points: _____ ,

___________ , and ________ .

Step-by-Step Solution

Answer

The three points are : $(a,1);(1,0) and (\frac{1}{a},-1)$

Step 1. Given information

Given expression is $f\left(x\right)={\log }_{a}x$

Step 2. Find the point

Let us assume, three points on the $x-axis$ are $a,1,\frac{1}{a}$

Now,

$$\begin{gathered} f\left(a\right)=1 \\ f\left(1\right)=0 \\ f\left(\frac{1}{a}\right)=-1 \end{gathered}$$

Hence, there points on the function are :$(a,1); (1,0) and (\frac{1}{a},-1)$

Step 3. Relevant picture