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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.6, Problem 33E

(a)

To determine

**To Explain:** The definition of the logarithmic function

Expert Solution

Let

**To prove:**

**Proof:**

Consider

Equating the powers on both sides,

Therefore, it is one to one and

Here
*x.*

Thus, the logarithm of *x* in base b is written for

(b)

To determine

**To find:** The domain of

Expert Solution

The domain of

Since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function.

The exponential function is always positive so logarithmic function is not definedfor negative numbers or for zero.

Therefore, the domain of the logarithmic function

(c)

To determine

**To find:** The range of

Expert Solution

**Solution:**

The range of

Since the logarithmic function is the inverse of the exponential function, the range of logarithmic function is the domain of exponential function.

The exponential function is defined for all real numbers so logarithmic function can take any real number.

Therefore, the range of the logarithmic function

(d)

To determine

**To sketch:** The graph of the function

Expert Solution

**Graph:**

Use online graph calculator and draw the graph of the function