BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.9, Problem 34E
To determine

To calculate: The value of x from the equation 4x+262x=52x+4 by algebraic method and graphical method.

Expert Solution

Answer to Problem 34E

The value of x is 23 and Graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 34E , additional homework tip  1

Explanation of Solution

Given information:

The equation 4x+262x=52x+4 .

Calculation:

It is provided that the equation 4x+262x=52x+4 .

Algebraic method;

The method in which isolate x on one side of the equation and solve the value of x .

From the equation 4x+262x=52x+4 ,

  4x+262x=52x+44.2x6(x+2)2x(x+2)=52(x+2)8x6x22x(x+2)=52(x+2)

Solve the value of x from the equation,

  8x6x22x(x+2)=52(x+2)2x22x(x+2)=52(x+2)x=23

Therefore, the value of x=23 .

Graphical method;

Let put y1=4x+262x and y2=52x+4

The graph of the equation y1=4x+262x provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 34E , additional homework tip  2

The graph of equation y2=52x+4 is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 34E , additional homework tip  3

The graph of both equations in same figure is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 34E , additional homework tip  4

The solution is the x coordinate of the intersection point (23,5)  of the two graphs. So, the intersection point on the x coordinate is 23 .

Thus, the value of x is 23 .

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