SOLUTION: ln x-ln(x+7)=-1

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Question 142208: ln x-ln(x+7)=-1
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

ln%28x%29-ln%28x%2B7%29=-1 Start with the given equation



ln%28%28x%29%2F%28x%2B7%29%29=-1 Combine the logs using the identity ln%28A%29-ln%28B%29=ln%28A%2FB%29



e%5E%28-1%29=%28x%29%2F%28x%2B7%29 Use the property ln%28x%29=y ==> e%5Ey=x to rewrite the equation



1%2Fe=%28x%29%2F%28x%2B7%29 Rewrite e%5E%28-1%29 as 1%2Fe



x%2B7=ex Cross Multiply


7=ex-x Subtract x from both sides


7=x%28e-1%29 Factor out the GCF x


7%2F%28e-1%29=x Divide both sides by e-1



So our answer is x=7%2F%28e-1%29 which is approximately x=4.07384

Answer by ankor@dixie-net.com(12692) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x)- ln(x+7) = -1
:
Same as
ln(x%2F%28x%2B7%29) = -1
:
Find e^ of both sides
x%2F%28x%2B7%29 = .36788
:
Multiply both sides by (x+7) and you have:
x = .36788(x+7)
:
x = .36788x + 2.5752
:
x -.36788x = 2.5752
:
.63212x = 2.5752
x = 2.5752%2F.63212
x = 4.074
:
:
Check solution on calc: enter ln(4.074) - ln(11.074) = -.99997 ~ -1