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Chapter 5: Q. 6 (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.

logx+6=1

Short Answer

Expert verified

The solution of the logarithmic equation is{4}.

Step by step solution

01

Step 1. Given information

Thegivenequationislogx+6=1.

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

02

Step 2. Simplify. 

Now,鈬�logx+6=1鈬�x+6=101鈬�x=10鈭�6鈬�x=4

03

Step 3. Verifying the result 

Plot the graph of the equation logx+6=1using the graphing utility.

From the above graph. we can observe that the graph of the given equation intersects the x-axis at x=4.

Therefore, the solution is verified.

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Most popular questions from this chapter

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)

The domain of one to one function g is0,15,and its range is0,8. State the domain and range ofg-1

A function fhas an inverse function. If the graph of f lies in quadrant II, in which quadrant does the graph of f-1lie?

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

f(x)=-3x-4x-2
See all solutions

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