Final answer:
We used the logarithmic property log(xy) = log(x) + log(y), ending up with the equation x + 18 = 18x. Solving that resulted in x = 18/17, which we then validated against the original problem.
Step-by-step explanation:
To solve the equation log(x+18)=log(x)+log(18), we use the property that the sum of the logarithms of two numbers is equal to the logarithm of the product of the two numbers. It is given by log xy = log x + log y. This means that log(x+18) = log(18x).
Therefore, the underlying equation for the problem is x + 18 = 18x. Solving this for x, we subtract x from both sides to get 18 = 17x. Then we divide both sides by 17, resulting in x = 18/17 or approximately x = 1.0588.
Please note: In logarithmic equations, you must always validate your solution in the original problem to avoid the logarithm of a negative number. As the value we found is positive, we don't have any issues here.
Learn more about Logarithmic Properties