Chapter 5: Q 6. (page 297)

If the graph of a logarithmic function $f (x) = \log_{a} x$ , where $a > 0$ and $a \neq 1$ , is increasing, then its base must be larger
than ___________ .

Short Answer

Expert verified

The base must be larger than $1$ .

Step by step solution

Step 1. Given information

Given expression is $f (x) = \log_{a} x$

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 $f (x) = \log_{0.9} x$ be monotonic decreasing as shown below :

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

Step 3. Relevant image

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If the graph of a logarithmic function $f (x) = \log_{a} x$ , where $a > 0$ and $a \neq 1$ , is increasing, then its base must be larger
than ___________ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Range of base

Step 3. Relevant image

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If the graph of a logarithmic function f(x)=logax, where a>0and a≠1, is increasing, then its base must be largerthan ___________ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Range of base

Step 3. Relevant image

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Probability and Statistics

Mechanics Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

If the graph of a logarithmic function $f (x) = \log_{a} x$ , where $a > 0$ and $a \neq 1$ , is increasing, then its base must be larger
than ___________ .