Explanation Given: The provided family of logarithmic functions is y = log a ( x ) where, a > 0 and a ≠ 1 . Graph: Consider the function, y = log a ( x ) Since, according to the properties of logarithms, this function is also equivalent to a y = x …… (1) Thus, first substitute 2 for a in equation (1). Then, the equation becomes x = 2 y Or, y = log 2 ( x ) Obtain the values of x by assuming some values of y as, For y = 0 , substitute in x = 2 y . x = 2 0 = 1 Thus, the point obtained is ( 1 , 0 ) . For y = 1 , substitute in x = 2 y . x = 2 1 = 2 Thus, the obtained point is ( 2 , 1 ) . For y = 2 , substitute in x = 2 y . x = 2 2 = 4 Thus, the obtained point is ( 4 , 2 ) Now, Construct a table for the values of y with the corresponding values of x as: x 1 2 4 y 0 1 2 Plot the graph for the fucntion, y = log 2 ( x ) . Now, substitute 3 for a in equation (1). Then, the equation becomes, x = 3 y Or, y = log 3 ( x ) Obtain the values of x by assuming some values of y as, For y = 0 , substitute in x = 3 y . x = 3 0 = 1 Thus, the point obtained is ( 1 , 0 ) . For y = 1 , substitute in x = 3 y . x = 3 1 = 3 Thus, the obtained point is ( 3 , 1 ) . For y = 2 , substitute in x = 3 y . x = 3 2 = 9 Thus, the obtained point is ( 9 , 2 ) Now, Construct a table for the values of y with the corresponding values of x as: x 1 3 9 y 0 1 2 Plot the graph for the fucntion, y = log 3 ( x )

6th Edition

ISBN: 9780321916600

Author: Mark Dugopolski

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 4.2, Problem 148E

To determine

To graph: The logarithmic function of the form y=loga(x) where, a>0 and a≠1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.2, Problem 147E

Chapter 4.2, Problem 149E

Chapter 4 Solutions

College Algebra (6th Edition)

Ch. 4.1 - True or False? Explain. The function f(x) =...Ch. 4.1 - True or False? Explain. 2. The function f(x) =...Ch. 4.1 - Prob. 3FT Ch. 4.1 - True or False? Explain. 4. If f(x) = 3x, then Ch. 4.1 - Prob. 5FT Ch. 4.1 - Prob. 6FT Ch. 4.1 - Prob. 7FT Ch. 4.1 - Prob. 8FT Ch. 4.1 - Prob. 9FT Ch. 4.1 - Prob. 10FT

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

To graph: The logarithmic function of the form y = log a ( x ) where, a > 0 and a ≠ 1 .

Solution Summary: The author explains the logarithmic function of y=mathrmlog_a(x) where, a>0 and ane 1.

Concept explainers

Videos

To graph: The logarithmic function of the form y=loga(x) where, a>0 and a≠1.

Want to see the full answer?

Chapter 4 Solutions

To graph: The logarithmic function of the form y = log a ( x ) where, a &gt; 0 and a ≠ 1 .

Solution Summary: The author explains the logarithmic function of y=mathrmlog_a(x) where, a>0 and ane 1.

Concept explainers

Videos

To graph: The logarithmic function of the form y=loga(x) where, a>0 and a≠1.

Want to see the full answer?

Chapter 4 Solutions

To graph: The logarithmic function of the form y = log a ( x ) where, a > 0 and a ≠ 1 .