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Chapter 5: Q. 31 (page 315)

In Problems 5鈥�32, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

logax-1-logax+6=logax-4-logax+3

Short Answer

Expert verified

The solution isx=4.5

Step by step solution

01

Step 1. Given information

The given equation is

logax-1-logax+6=logax-4-logax+3
02

Step 2. Simplify and solve

logax-1-logax+6=logax-4-logax+3鈬�logax-1x+6=logax-2x+3鈬�x-1x+3=x-2x+6鈬�x2+2x-3=x2+4x-12鈬�-2x=-9鈬�x=4.5

03

Step 3. Verify the solution

The graph of the given equation is,

The graph is a vertical line x=4.5.

Hence the solution is correct.

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