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Chapter 5: Q. 9 (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.

log4x+2=log48

Short Answer

Expert verified

The solution of the equation is{6}.

Step by step solution

01

Step 1. Given information

Thegivenequationislog4x+2=log48.

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,Weknow,鈬�logab=logbloga.Thus,鈬�log4x+2=log48鈬�logx+2log4=log8log4鈬�logx+2=log8鈬�x+2=8鈬�x=8鈭�2鈬�x=6

03

Step 3. Verifying the result

Plot the graph of the equation log4x+2=log48using the graphing utility.

From the above graph. we can observe that the graph of the given equation intersects the x-axis atx=6

Therefore, the solution is verified.

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