EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Equations and inequalities describe the relationship between two mathematical expressions.

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Question

Chapter 3.4, Problem 3E

(a)

To determine

To find: Whether the given value of x is a solution of the equation or not.

(a)

Expert Solution

Answer to Problem 3E

The x -value, x=5 is solution of the equation 42x−7=64 .

Explanation of Solution

Given information:

The equation 42x−7=64 and x -value x=5 .

Formula used:

Substitute the provided value of the variable in the function to check whether left hand side of the equation is equal to right hand side of the equation.

Calculation:

Consider the provided equation 42x−7=64 and x -value that is x=5 .

Substitute x as 5 in the left hand side of the above equation,

42x−7=6442(5)−7=64410−7=6443=64

Simplify it further as,

64=64

The above equation is true.

Therefore, x=5 satisfy the equation 42x−7=64 .

Hence, the x -value, x=5 is solution of the equation 42x−7=64 .

(b)

To determine

To find: Whether the given value of x is a solution of the equation or not.

(b)

Expert Solution

Answer to Problem 3E

The x -value, x=2 is not a solution of the equation 42x−7=64 .

Explanation of Solution

Given information:

The equation 42x−7=64 and x -value x=5 .

Formula used:

Substitute the provided value of the variable in the function to check whether left hand side of the equation is equal to right hand side of the equation.

Calculation:

Consider the provided equation 42x−7=64 and x -value that is x=2 .

Substitute x as 2 in the left hand side of the above equation,

42x−7=6442(2)−7=6444−7=644−3=64

Simplify it further as,

143=64164=64

The above equation is false as 164≠64 .

Therefore, x=2 does not satisfy the equation 42x−7=64 .

Hence, the x -value, x=2 is not a solution of the equation 42x−7=64 .

(c)

To determine

To find: Whether the given value of x is a solution of the equation or not.

(c)

Expert Solution

Answer to Problem 3E

The x -value, x=12(log464+7) is a solution of the equation 42x−7=64 .

Explanation of Solution

Given information:

The equation 42x−7=64 and x -value x=12(log464+7) .

Formula used:

Substitute the provided value of the variable in the function to check whether left hand side of the equation is equal to right hand side of the equation.

The inverse property of logarithmic function is logaax=x .

Calculation:

Consider the provided equation 42x−7=64 and x -value that is x=12(log464+7) .

Substitute x as 12(log464+7) in the left hand side of the above equation,

42x−7=6442(12(log464+7))−7=644log464+7−7=644log464=64

Recall the inverse property of logarithmic function that is logaax=x .

Apply it,

4log443=6443=6464=64

The above equation is true.

Therefore, x=12(log464+7) satisfy the equation 42x−7=64 .

Hence, the x -value, x=12(log464+7) is a solution of the equation 42x−7=64 .

Chapter 3.4, Problem 2E

Chapter 3.4, Problem 4E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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