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???)

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