SOLUTION: logx=1-log(x-3)
what is the value of x?
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Question 277250: logx=1-log(x-3)
what is the value of x?
Found 2 solutions by nerdybill, dabanfield:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
logx=1-log(x-3)
.
applying the "log rules":
logx=1-log(x-3)
logx+log(x-3) = 1
log[x(x-3)] = 1
x(x-3) = 10^1
x^2-3x = 10
x^2-3x-10 = 0
factoring
(x-5)(x+2) = 0
x = {-2,5}
.
We can toss out the -2 -- because plugging it back into the original eq we will get a log of a neg number -- no good -- this is called an "extraneous solution".
.
So, we conclude:
x = 5
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
logx=1-log(x-3)
log x + log (x-3) = 1
log (x*(x-3)) = 1
If the base is 10 then we have by definition of a log:
x*(x-3) = 10^1
x^2 - 3x = 10
x^2 - 3x - 10 = 0
(x-5)*(x+2) = 0
x-5 = 0 or x+2 = 0 so
x = 5 and/or x = -2
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