SOLUTION: 1. Solve the following equations a) log x+1 = log 6 - log x b) ln(x-2) +ln3 = ln(x+1) Can you please help me out? Thanks so much in advance:) Can you please show all the step

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Solve the following equations a) log x+1 = log 6 - log x b) ln(x-2) +ln3 = ln(x+1) Can you please help me out? Thanks so much in advance:) Can you please show all the step      Log On


   

Question 744481: 1. Solve the following equations
a) log x+1 = log 6 - log x
b) ln(x-2) +ln3 = ln(x+1)
Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. Solve the following equations
a) log x+1 = log 6 - log x
Subtracting logs means divide so we can combine on the right to
log(x+1) = log%28%286%2Fx%29%29
if the logs are equal, the values are equal, therefore:
x + 1 = 6%2Fx
multiply both sides by x
x(x+1) = 6
arrange as a quadratic equation
x^2 + x - 6 = 0
Factors to
(x+3)(x-2)
Two solutions
x = -3
x = +2, this is the only solution, (we can't find the log of a neg number)
:
Check this on a calc:
enter: log(2+1) results: .477..
then
enter: log(6) - log(2): results: .477..; equality confirms our solution of x=2
:
:
b) ln(x-2) + ln(3) = ln(x+1)
Adding logs is multiply, combine on the left
ln(3(x-2)) = ln(x+1)
ln(3x-6) = ln(x+1)
therefore
3x - 6 = x + 1
3x - x = 1 + 6
2x = 7
x = 7/2
x = 3.5
:
:
Check this on a calc replace x with 3.5:
enter: ln(3.5-2) + ln(3); results: 1.504..
enter: ln(3.5+1); results: 1.504.. confirms our solution of x=3.5
:
Are you understanding this better now? C