Question

solve for x: logx=1 - log(x-3)​

Answer 1

here is your answer

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Answer 2

Hyy Dude

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

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

Hope it's helps you

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