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Chapter 5: Q. 8 (page 315)

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

log33x鈭�1=2

Short Answer

Expert verified

The solution of the logarithmic equationlog33x鈭�1=2is103or3.333

Step by step solution

01

Step 1. Given information

Thegivenequationislog33x鈭�1=2.

We have to express irrational solutions in exact form and as a decimal rounded to three decimal places.

Also, we have to verify the result using the graphing utility.

02

Step 2. Simplify.

Now,Wecanwrite,鈬�logab=casb=ac.Thus,鈬�log33x鈭�1=2鈬�3x鈭�1=32鈬�3x鈭�1=9鈬�3x=9+1鈬�3x=10鈬�x=103鈬�x=3.333

03

Step 3. Verifying the result

Plot the graph of the equation log33x鈭�1=2using the graphing utility.

From the above graph. we can observe that the graph of the given equation intersects the x-axis at x=103or3.333.

Therefore, the solution is verified.

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Most popular questions from this chapter

the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x-4x-2

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

The graph of an exponential function is given. Match each graph to one of the following functions.

As the base a of an exponential function fx=ax, where a>1increases, what happens to the behavior of its graph forx>o?What happens to the behavior of its graph for x<0?

Use a calculator to compute the various values of the expression. Compare the values to e.

2+11+12+23+34+4etc
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