SOLUTION: 8. Solve and Check the Following Equations: C. log6 x + log6 (x � 2) = log6 15

Question 113826: 8. Solve and Check the Following Equations:
C. log6 x + log6 (x � 2) = log6 15
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

Distribute

Since the base of the logs are equal, the arguments (the stuff inside the logs are equal). So

So let's solve

Start with the given equation

Subtract 15 from both sides

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 solutions are or

However, since you cannot take the log of a negative number, the only solution is

-------------------------------------
Check:

Let's check the solution

Start with the equation found on the third step.

Plug in

Square and multiply

Subtract. Since both sides of the equation are equal, this solution is verified.

So the solution is verified

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