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Chapter 5: Q. 71 (page 284)

solve equation. Verify your results using a graphing utility.

8-x+14=16x

Short Answer

Expert verified

The value of x for which the equation is valid is 6.

Step by step solution

01

Step 1. Given equation

8-x+14=16x

02

Step 2. Solving the equation using exponential properties 

8-x+14=16x23(-x+14)=24(x)2(-3x+42)=2(4x)

By exponential property

av=au⇒v=u

Using this :

-3x+42=4x⇒7x=42⇒x=6

We get value of x :

6

03

Step 3. Verifying Graphically

Sketching the graphs of

8-x+14=16x

Where they will intersect will be the solution .

these graph intersect at (6,16777216 )

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Most popular questions from this chapter

The domain of one-to-one function g is0,15, and range is (0,8). State the domain and range oflocalid="1646180141229" g-1

If 2x=3, what does4-xequal?

Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

W(h)=50+2.3h-60

(a) What is the ideal weight of a 6-foot male?

(b) Express the height has a function of weight W.

(c) Verify that h=Whis the inverse of W=Whby showing that role="math" localid="1646158219737" h(W(h))=h and W(h(W))=W.

(d) What is the height of a male who is at his ideal weight of 80 kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" Wh=45.5+2.3(h-60).

Find the domain of the functionf(x)=x2-1x2-25.

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=2x3x-1
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