Question

If the graph of a logarithmic function $f\left(x\right)={\log }_{a}x$, where $a>0$and $a\ne 1$, is increasing, then its base must be larger

than ___________ .

Short answer

The base must be larger than$1$.

Step-by-step solution

Step 1. Given information

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

Step 2. Range of base

Let us assume, the base of logarithmic function 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. Relevant image