SOLUTION: I need help solving this logarithmic equation log(x-14)-log5=log(x-12)-logx

Question 129944: I need help solving this logarithmic equation
log(x-14)-log5=log(x-12)-logx
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Combine the logs using the identity

Raise both sides as exponents with bases of 10 to eliminate the logs on both sides

Multiply both sides by to eliminate the fractions

Multiply

Distribute

Subtract 5x from both sides. Add 60 to both sides.

Combine like terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our possible answers are
or

However, if you plug in into , you'll get a negative number inside the log. So our only solution is

-----------------------------------

Answer:

So our answer is

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