Q6. - Precalculus Enhanced with Graphing Utilities

Question

If the graph of a logarithmic function $f\left(x\right)={\log }_{a}x$, where $a>0$ and $a\ne 0$, is increasing, then its base must be larger than_____. 

Step-by-Step Solution

Answer

The base must be larger than 1.

Step 1. Given information.

Consider the given information.

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

Step 2. Range of base.

Let us assume, that the base of the logarithmic function is less than 1, say 0.9.

Now, the graph of the function $f\left(x\right)={\log }_{0.9}x$be monotonic decreasing as shown below :

Hence, The base number must be greater than 1 to be an increasing function.

Step 3. Draw the graph.

Draw the graph of the function.