Common "log" mistake

Teacher: John, can you give the answer for X in this log X = log 6 question?

John: No problem. The value for X is simply 6.

Teacher: Correct! How did you get the answer?

John: It is easy. Just do it this way
(John wrote on the board). ==> X = (log 6) /log ==>X = 6.

Teacher: ?????

************************* What happened? ***********************

Logarithm or "log", in its abbreviated form, can be easily misunderstood.

What is this "log"?

Logarithm is an operation on a number that is the reverse of that for indexing a number.

Log_aX = Y ==> a^Y = X

From the above relationship, you will notice that "log" itself cannot stand alone.

That means "log" must come with a number or expression.

"Log" is an operator, like the "+" or "-".

What mistake did John made?

John mis-interpreted the "log" to be a variable!

It made him transfer the "log" over the equal symbol as though it is a number (or equivalent).
the "log" is thus, separated from the "X" that it should operate upon.

A common "log" mistake was made.

Correct answer:
The answer can be obtained through logically comparison, that is,
when log X = log 6, X is simply = 6.

The question may be simple, but if the learning is improper, the concept behind it may be drastically, wrong, even though the answer can be correct.

Learn well. Maths does not call for correct answer. It is the thinking behind it.

..... :-)