# Do You {heart} Logarithms?

Me, not so much…

$\log_5(x+8) - log_5(x+4)= 1\\ \log_5(x+8)(x+4)=1\\ \log_5(x^2+12x+32)=1\\ 5=x^2+12x+32\\ 0=x^2+12x+27\\ 0=(x+9)(x+3)\\ x\neq -9, x=-3$

So… the question I have for you is WHY can’t x = -9, but x = -3 is correct? (I got it, but it took a while, sheesh… what kind of homeschooling mom am I, anyway???)