SOLUTION: Can you please show me the steps to solve ln10-ln(2x+10)=3 ? Here is what I have tried so far: ln10/2x+10=3 (Quotient Property) log base e of 10/2x+10=3 (ln is the same

Question 740011: Can you please show me the steps to solve ln10-ln(2x+10)=3 ?
Here is what I have tried so far:
ln10/2x+10=3 (Quotient Property)
log base e of 10/2x+10=3 (ln is the same as log base e)
e^3=10/2x+10 (change to exponential form)
e^3(2x+10)=10 (multiply both sides by 2x+10)
2x+10=10/e^3 (divide both sides by e^3)
2x=10/e^3 -10 (subtract ten from both sides)
x=(10/e^3 -10)/2 (divide both sides by 2)
after plugging everything into a calculator, my answer was about -4.75
Is this the right answer? Is there an easier way to solve this? My teacher put {(5-5e^3)/e^3} as his answer. Why did his answer come out in this format?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Both forms are correct.
.
Starting with your form:
x=(10/e^3 -10)/2
dividing each term by 2:
x= 5/e^3 - 5
common denominator is e^3:
x= 5/e^3 - 5(e^3/e^3)
x= 5/e^3 - (5e^3)/e^3
x= (5 - 5e^3)/e^3 (which is your teacher's format)

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