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Chapter 5: Q. 43 (page 349)

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:log6(x+3)+log6(x+4)=1

Short Answer

Expert verified

The solution set ofx=-1

Step by step solution

01

Step 1. Given information  

An equation,log6(x+3)+log6(x+4)=1

02

Step 2. Required to find 

Solve the given equation to find x.

03

Step 3. Solving the equation 

Given, log6(x+3)+log6(x+4)=1

role="math" localid="1646577602947" 鈬�log6(x+3)(x+4)=1

鈬�(x+3)(x+4)=61

鈬�x2+4x+3x+12=6

鈬�x2+7x+12-6=0

鈬�x2+7x+6=0

鈬�(x+6)(x+1)=0

鈬�x=-6,x=-1

But, x+3>0or x>-3

Therefore,x=-1

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