Can someone help me with this logarithm? Asked this earlier =(

log[5](x+116)=4-log[5](x-4)

Question

Can someone help me with this logarithm? Asked this earlier =(

log[5](x+116)=4-log[5](x-4)

vijay · Answer

20 = (x-4) * (x+116) solve this

anonymous · Answer

are u sure its 20 and not 5^4?

anonymous · Answer

Eh.. that's wrong, sorry.

anonymous · Answer

$log_5(x+116) = 4 - log_5(x-4)$$$\implies log_5(x+116) + log_5(x-4) = 4$$$$\implies log_5((x+116)(x-4)) = 4$$$$\implies (x+116)(x-4) = 5^4$$

vijay · Answer

$$\log(5) (x+116) + \log(5)(x-4 ) = \log(5) (5^{4})$$

anonymous · Answer

yes polpok thats what i meant. I got to that point and im trying to solve. I got stumped. Because I know (x=116)(x-4)=625 then i need to solve and make the equation equal to zero so i can factor then correct?

anonymous · Answer

foil out the left hand side, then subtract 625 from both sides and solve the quadratic.

anonymous · Answer

According to my book i need to factor and i'm stumped at that point. 

i'm at.... x^2+120x-161=0  trying to factor for the final answer..lost

anonymous · Answer

If factoring seems too painful I suggest just using the quadratic formula. Do you know it?

anonymous · Answer

yes i'm just trying to go by the book.

anonymous · Answer

Although I disagree with that quadratic..

anonymous · Answer

Disagree as in it is incorrect from that point?

anonymous · Answer

You should have:
        $(x+116)(x-4) = 625$
$$\implies x^2 +112x - 464 = 625$$$$\implies x^2 + 112x - 1089 = 0$$

anonymous · Answer

I think you messed up your signs when you foiled

anonymous · Answer

Ugh thank you...i did miss the subtraction. i had it on paper as another plus. u caught it thanks

anonymous · Answer

@Polpak..I had a much easier time solving with the quadratic formula thank u!!