Please tell me if I am doing this equation right or not! Help!?

Question

(a) Given that log (base 3) x - log (base 3) (x-5) = log (base 3) A, express A in terms of x.

This is how I am doing this:

log (base 3) x - log (base 3) (x-5) = log (base 3) A

= log (base 3) x / (x-5) = log (base 3) A

I canceled out the x on the fraction.

= log (base 3) (1/-5) = log (base 3) A

The bases cancel out...

= (1/-5) = A

That is what I got A as. Now I look back at the question and it says to express the answer in terms of x. I don't have an x in my answer...

Is this right? If not, please teach me your solution.

Thanks! I am choosing best answer. :)

Answer 1

log (base 3) x - log (base 3) (x-5) = log (base 3) A

==> log (base 3) x / (x-5) = log (base 3) A

==> (x / x-5) = A

I just copied here your answer and corrected some mistakes

You know how to work with logarithm now, the only mistake is on algebraic operation. You also misused the = sign where I replaced it with ==> (you can read: it follows that)

Answer 2

you cannot cancel x there...

log3 (x/(x-5))=log3 (A)

    so, A=(x/(x-5))

Answer 3

exactly what the person above me said

you cannot cancel the x so it becomes log base 3 to the x/x-5=log base 3 to the A

CANCEL OUT THE LOG BASES ON BOTH SIDES

x/x-5=A

there you expressed A in terms of x

Answer 4

You almost got it..........Except that you cannot reduce x/(x-5) to 1/-5

Log (x/(x-5)) = Log A

A = x/(x-5)