SOLUTION: Solve for x: log(base 5)3x + log(base 5)(x-3) = 1 I see they both have a common base of 5. I'm not sure if I'm on the right track, but this is what I got so far: log(base 5)[3

Question 80522: Solve for x: log(base 5)3x + log(base 5)(x-3) = 1
I see they both have a common base of 5. I'm not sure if I'm on the right track, but this is what I got so far:
log(base 5)[3x(x-3)] = 1
3x(x-3) = 5^1
3x^2 - 9x =5
3x^2 - 9x - 5 = 0
I then tried factoring it out, but I don't think it works.
I think that first 3 in the problem might be throwing me off for some reason. Any help with this is greatly appreciated. Thanks.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:
Apply the product rule for logarithms.
Simplify the left side.
Rewrite in exponential form.
Subtract 5 from both sides.
Your work up to this point is commendable!...and you are correct, this quadratic equation is not factorable, so you can use the quadratic formula:

The exact answers are:

The approximate answers are:
To the nearest hundredth.
To the nearest hundredth.
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