# Algebra II : Graphing Logarithmic Functions

## Example Questions

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### Example Question #1 : Graphing Logarithmic Functions

Give the -intercept of the graph of the function

to two decimal places.

The graph has no -intercept.

Explanation:

Set  and solve:

The -intercept is .

### Example Question #2 : Graphing Logarithmic Functions

Give the  intercept of the graph of the function

to two decimal places.

The graph has no -intercept.

Explanation:

Set  and solve:

The -intercept is .

### Example Question #1 : Graphing Logarithmic Functions

What is/are the asymptote(s) of the graph of the function  ?

and

and

Explanation:

The graph of the logarithmic function

has as its only asymptote the vertical line

Here, since , the only asymptote is the line

.

### Example Question #2 : Graphing Logarithmic Functions

Evaluate

Explanation:

Use the change of base formula for the logarithmic function.

Or

can be solved using .

### Example Question #5 : Graphing Logarithmic Functions

Evaluate

Explanation:

Use the change of base formula for logarthmic functions.

Or

can be solved using

### Example Question #3 : Graphing Logarithmic Functions

Solve for

No real solutions

Explanation:

Use the change of base formula for logarithmic functions and incorporate the fact that  and

Or

can be solved using

### Example Question #7 : Graphing Logarithmic Functions

Solve for

Explanation:

Use the change of base formula for logarithmic functions to solve this problem.

Or

can be solved using

For this specific problem we need to remember that  gives an unreal number therefore is not our answer.

Thus,

.

### Example Question #4 : Graphing Logarithmic Functions

Evaluate

Explanation:

Use the change of base formula for logarithmic functions.

Or

can be solved using

### Example Question #5 : Graphing Logarithmic Functions

Solve for

Explanation:

Use the change of base formula for logarithmic functions.

Or

can be solved using

### Example Question #10 : Graphing Logarithmic Functions

Which is true about the graph of

?

The range of the function is infinite in both directions positive and negative.

The domain of the function is greater than zero

None of the answers are correct

All of the answers are correct

When  ,  is twice the size as in the equation

All of the answers are correct

Explanation:

There is no real number  for which

Therefore in the equation  ,  cannot be

However,  can be infinitely large or negative.

Finally, when   or twice as large.

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