SOLUTION: Solve. Round to the nearest 100ths if necessary. log6(x)+log6(x+5)=2

I interpret the given equation this way

     +  = 2.


Using properties of logarithms, rewrite it this way

    x*(x+5) = ,

    x*(x+5) = 36,

    x^2 + 5x - 36 = 0.


At this point, you can solve this quadratic equation using the quadratic formula.
Alternatively, you can solve it using factoring

    (x+9)*(x-4) = 0,

     x = -9  or  x = 4.


The negative root does not work, since 'x' is under the logarithm, so we reject this root.

The other root, x = 4, works perfectly, as you can see when substituting it into the original equation.

Then the left side is

     +  =  +  =  =  =  = 2,

the same as the right side.


ANSWER.  The given equation has a unique solution  x = 4.