Question

What is the solution of ln(x+6)-ln9=2

x=53.50
x=60.50
x=66.50
x=72.50

Answer 1

B: 60.50

Explanation:

On edg

Answer 2

ln(x+6)-ln9=2

Using ln(a/b)=lna-lnb; with a=x+6 and b=9:
ln[(x+6)/9]=2

Using ln a=b→a=e^b; with a=(x+6)/9 and b=2, where e=2.718281828
(x+6)/9=e^2

Solving for x. Multiplying both sides of the equation by 9:
9[(x+6)/9]=9(e^2)
x+6=9e^2

Subtracting 6 both sides of the equation:
x+6-6=9e^2-6
x=9e^2-6

Replacing e=2.718281828
x=9(2.718281828)^2-6
x=9(7.389056096)-6
x=66.50150486-6
x=60.50150486

Rounded to the nearest hundreth:
x=60.50

Answer: Second option x=60.50