Solve the logarithmic equation. Express your solutions in exact form only. Please show all of your work.
log3(x+10)+log3(x-3)-2=log3(x-2)

Question

anonymous · Answer

$$ \log_{3}{(x+10)}+log_{3}{(x-3)}-2= log_{3}{(x-2)}$$
$$ 3^{\log_{3}{(x+10)}+log_{3}{(x-3)}-2}= 3^{log_{3}{(x-2)}}$$
$$ ((x+10)*(x-3))*3^{-2}= (x-2) $$
$$ x^{2}+7x-30= 3^{2}(x-2) $$
$$ x^{2}-2x-48=0 $$
$$(x-8)(x+6)=0$$
$$x=\{8, -6\}$$


Plug both answers into the original equation to check for extraneous roots. I skipped a few steps, but am sure you can fill them in, remember the rules for logs when going through this.

anonymous · Answer

Thank you. :)