SOLUTION: Please help me solve the following... log6(6 is lower than the g) (x+3) + log6(6 is lower to the g)(x+4)=1

Question 149549: Please help me solve the following...
log6(6 is lower than the g) (x+3) + log6(6 is lower to the g)(x+4)=1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Combine the logs on the left side using the identity

FOIL

Rewrite the equation using the property: ====>

Simplify

Subtract 6 from both sides.

Combine like terms.

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

Since we cannot take the log of a negative number, this means that we must disregard the solution . Notice how

So the only solution is
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