Answer
The solution set is $\{2\}$.
Work Step by Step
The given equation is
$\log x + \log (x+3) = \log 10$
Use product rule.
$\log x(x+3) = \log 10$
$ x(x+3) = 10$
Use the distributive property.
$x^2+3x=10$
Subtract $10$ from both sides.
$x^2+3x-10=10-10$
Simplify.
$x^2+3x-10=0$
Factor
$x^2+5x-2x-10=0$
$x(x+5)-2(x+5)=0$
$(x+5)(x-2)=0$
Set both factors equal to zero.
$x+5=0$ or $x-2=0$
Isolate $x$.
$x=-5$ or $x=2$.
$-5$ does not exist in the logarithmic function domain.
Hence, the solution is $x=2$.
