To solve this equation, we can use the property of logarithms that states that if loga(b) = loga(c), then b = c.

Therefore, we can set the exponents on both sides of the equation equal to each other:

x^2 - 4x - 5 = 7 - 3x

Next, we can simplify the equation by combining like terms:

x^2 + 3x - 12 = 0

Now we have a quadratic equation that we can solve using the quadratic formula:

x = [-3 ± sqrt(3^2 - 4(1)(-12))] / 2(1)
x = [-3 ± sqrt(9 + 48)] / 2
x = [-3 ± sqrt(57)] / 2

Therefore, the solutions to the equation are:

x = (-3 + sqrt(57)) / 2
x = (-3 - sqrt(57)) / 2

These are the two possible values for x that satisfy the original equation.