Question 1061200: Log(4+x)-log(x-5)=log2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! log(4+x) is the same as log(x+4)
you get log(x+4) - log(x-5) = log((x+4)/(x-5))
therefore:
log((x+4)/(x-5)) = log(2)
this is true if and only if (x+4)/(x-5) = 2
solve for x to get x = 14.
replace x with 14 to see that the original equation is true.
log(x+4) = log(18).
log(x-5) = l0og(9).
you get log(18) - log(9) = log(2).
evaluate log(18) - log(9) to get .3010299957
evaluate log(2) to get .3010299957.
they're the same, so the value of x = 14 is confirmed to be good.
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