log x + log (x + 3) = 1

To solve the equation log x + log (x + 3) = 1, we can use logarithmic properties to simplify it.

First, we can apply the product rule of logarithms, which states that the logarithm of the product of two numbers is equal to the sum of their logarithms. In this case, we can rewrite the equation as a single logarithm:

log x + log (x + 3) = log (x * (x + 3))

Next, we can apply the logarithmic identity:

log a = b is equivalent to 10^b = a

Using this identity, we can rewrite the equation as:

10^1 = x * (x + 3)

Simplifying further:

10 = x^2 + 3x

This equation is now a quadratic equation that we can solve by setting it equal to zero:

x^2 + 3x - 10 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use factoring:

(x + 5)(x - 2) = 0

Now we have two possible solutions:

x + 5 = 0 or x - 2 = 0

Solving for x in each equation:

x = -5 or x = 2

Therefore, the solutions to the equation log x + log (x + 3) = 1 are x = -5 and x = 2.