Michael J. answered 04/22/16
Best Afterschool Tutor to Prepare You For Your Regents
Using the properties of logs, we can condense the equations so that we have a single log. Also, the solution to a logarithm is the exponent of the log's base number.
log6(x(x + 1)) = 1
log6(x2 + x) = 1
61 = x2 + x
6 = x2 + x
Subtract 6 on both sides of the equation.
0 = x2 + x - 6
Now you have a quadratic equation. Factoring, we get
0 = (x + 3)(x - 2)
Solving for x from this equation.
x = -3 and x = 2
Plug in these values into the equation to validate them.
log6((x + 2)(x + 3)) = 1
log6(x2 + 5x + 6) = 1
61 = x2 + 5x + 6
6 = x2 + 5x + 6
x2 + 5x = 0
We have a quadratic equation again. Factoring, we get
x(x + 5) = 0
Solve for x. I leave this part to you to finish.