Logs!

Which of the following is a solution to the equation log 4 x + log 4 (x – 3) = 1 ?

x = –3
x = 6/5
x = 2
x = 4

Question

Logs!

Which of the following is a solution to the equation log 4 x + log 4 (x – 3) = 1 ?

   x = –3 
   x = 6/5 
   x = 2 
   x = 4

anonymous · Answer

put it as 4^(left side) = 4^(right side)

this would get rid of the logs and you should be able to solve it quite easily afterwards.

anonymous · Answer

wait....did you mean log base 4?

anonymous · Answer

if not, use 10^(left side) = 10^right side

anonymous · Answer

Yes, log base 4

anonymous · Answer

$$f(x) = \log_{4} x + \log_{4} (x-3) = 1$$      This

anonymous · Answer

4^log4 x* 4^log4 (x-3) = 4^1

x (x-3) = 4

anonymous · Answer

So, x = 4?

anonymous · Answer

:) yep.

anonymous · Answer

Thanks!

anonymous · Answer

@Puzzhang, Be careful 

If x (x-3) = 4, then
$$x^2-3x-4 =0$$
$$(x-4)(x+1)=0$$
Then x=4 or x= -1

@rebercca14

anonymous · Answer

true. but since it was a multiple choice question.....agreed there would be both those answers in any other circumstance though.

anonymous · Answer

I mean the exact answer :D the x=-1 is not in the options.  Just saw now.  make sure you don't teach this way because if it is multi choice multi correct option, then the person whom you taught this will never know two solutions exist

anonymous · Answer

Also x cannot be -1 as log (negative quantity) is not posible.  So only x=4 is the solution