log x+log(x-9)=1

Question

The answer.

Answer 1

Assume log base is 10.

log₁₀(x(x-9))=1 is possibly another way of writing the equation.

x²-9x=10¹=10, x²-9x-10=0=(x-10)(x+1), so x=-1 or 10, but log(x) cannot be evaluated when x<0. So x=10 should be the solution.

log₁₀(x)+log₁₀(x-9)=1+log₁₀(1)=1+0=1 checks out OK.