is 2logx/2 = logX?

Answer 1

Brackets are required to clarify question.
There are two options:-

Option 1
2 log (x/2) = log [ (x/2)² ] = log (x² / 4)

Option 2
(2 log x) / 2 = log x

Take your pick as you know what you are asking.
However it is a good idea to use brackets to avoid confusion.

Answer 2

It depends on what you mean by your QUITE UNCLEAR NOTATION!

By crowding everything together without the slightest use of spacing or parentheses to make your meaning clear, you have challenged your readers to help unravel a very confused mind. Nevertheless, I shall do my best to help you.

(i) Clearly, for example, (2 log x) / 2 = log x.

THAT is a simple mathematical IDENTITY.

(ii) However, 2 log (x/2) = 2 log x - log 4.

That is another MATHEMATICAL IDENTITY. It differs from the first one merely because the clarifying parentheses have now been placed in different positions.

(It is no good arguing that you DELIBERATELY didn't use parentheses because you didn't want people to make one or the other of these two possible interpretations. That would be tantamount to saying that you don't give a damn whether you communicate clearly. Without taking some care in communication, your intentions are simply obscured.)

The second quite valid interpretation (2 log x - log 4) COULD be log x IF

2 log x - log 4 = log x.

THAT is now a MATHEMATICAL EQUATION, rather than an identity.

Its solution is given by:

log x = log 4, or, simply, x = 4.

CHECK of this solution:

If x = 4, 2 log (x/2) = 2 log 2 = log 4, which is clearly correct.

You now have two possible valid answers. Which one is appropriate depends on the interpretation you wished to be put upon your original question. Please try to anticipate readers' difficulties in future, by examining the questions you pose for possible ambiguities and taking the necessary steps to avoid them.

Live long and prosper.

Answer 3

no.

2logx/2 = log(x/2) ^2 != logx

Answer 4

technically the 2's cancel. but I haven't done logs in a long time!