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Asked Sep 2, 2019
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In Problems 43-51, solve and give the solutions in interval notation.

50. log(2x-5) 3
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50. log(2x-5) 3

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Expert Answer

Step 1

We first rise both sides to the power 10. 

log and 10 cancels. 

log(2x-5)3
Oг, 100E2x-5)<10°
Or, 2x-5 1000
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log(2x-5)3 Oг, 100E2x-5)<10° Or, 2x-5 1000

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Step 2

Then add 5 to both sides and divide by 2. 

2x-5 1000
Or, 2x1005
1005
Or, x
2
Or, x502.5
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2x-5 1000 Or, 2x1005 1005 Or, x 2 Or, x502.5

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Step 3

Inside log we can't have negative number. So, 2x-5>...

2х-5>0
Or, 2x>5
5
Or, x>
2
Or, x>2.5
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2х-5>0 Or, 2x>5 5 Or, x> 2 Or, x>2.5

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