SOLUTION: 1.Solve the following equations: (i) ln x + ln(x + 4) = ln(x + 6) (ii) 7^x+3 = e^x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1.Solve the following equations: (i) ln x + ln(x + 4) = ln(x + 6) (ii) 7^x+3 = e^x      Log On


   

Question 1189365: 1.Solve the following equations:
(i) ln x + ln(x + 4) = ln(x + 6)
(ii) 7^x+3 = e^x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1.Solve the following equations:
(i) ln x + ln(x + 4) = ln(x + 6)
ln(x*(x+4)) = ln(x+6)
x^2 + 4x = x+6
x^2 + 3x = 6
x^2 + 3x + 2.25 = 8.25
(x + 1.5)^2 = 8.25
x+1.5 = sqrt(33)/2, -sqrt(33)/2
x = (-3 + sqrt(33))/2 =~ 1.37228
The other "solution" is negative and is not valid due to the logarithm.
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(ii) 7^x+3 = e^x
Is x the exponent of 7?
Or x+3?