Question 45455
log x + log (x+9) = 1

You have a log rule which says log a + log b = log ab

So, you write:

 log x(x+9) =1

You know a transformation which says 

log b = c means  the same as b=10^c

So you write:
x(x+9)=10^1
x^2+9x-10=0
(x+10)(x-1)=0

Cheers,
Stan H.
x=-10 or x=1

You check these answers in the original equation
and see that x=-10 cannot be a solution because you
cannot have the log of a negative number.

So, x=1 is the only solution of your original equation.

Cheers,
Stan H.