To solve this equation, first use the properties of logarithms to combine the terms on both sides of the equation.
lg(3x-7) + lg(2) = lg(x+3) + lg(x-3)lg(2(3x-7)) = lg((x+3)(x-3))
Now apply the properties of logarithms to simplify the equation further:
lg(6x - 14) = lg(x^2 - 9)
Since the logarithms on both sides are equal, the expressions inside the logarithms must also be equal:
6x - 14 = x^2 - 9
Rearrange the equation into a quadratic form:
x^2 - 6x - 5 = 0
Now, we can factor the quadratic equation or use the quadratic formula to solve for x.
To solve this equation, first use the properties of logarithms to combine the terms on both sides of the equation.
lg(3x-7) + lg(2) = lg(x+3) + lg(x-3)
lg(2(3x-7)) = lg((x+3)(x-3))
Now apply the properties of logarithms to simplify the equation further:
lg(6x - 14) = lg(x^2 - 9)
Since the logarithms on both sides are equal, the expressions inside the logarithms must also be equal:
6x - 14 = x^2 - 9
Rearrange the equation into a quadratic form:
x^2 - 6x - 5 = 0
Now, we can factor the quadratic equation or use the quadratic formula to solve for x.