Final answer:
The given logarithmic equation is solved by using properties of logarithms to combine terms and solve for x. However, the calculated solution x = -6 is not valid for a logarithmic function since the argument cannot be negative, therefore the equation has no real solutions.
Step-by-step explanation:
To solve the equation log(5x) = log(3) + log(x - 4), we can use the properties of logarithms. The property that log(a) + log(b) = log(ab) allows us to combine the right side of the equation:
log(3) + log(x - 4) = log(3(x - 4))
Now we have:
log(5x) = log(3(x - 4))
Since the logarithms are equal, the arguments must be equal as well:
5x = 3(x - 4)
Expanding and solving for x:
5x = 3x - 12
2x = -12
x = -6
However, since x cannot be negative in log(x - 4) because the logarithm of a negative number is undefined, this solution is not valid within the real number system. Thus, there is no solution to the equation in real numbers.