Logical Comparison in Maths

Given a maths question, most of us will attempt solving it step by step, diligently, using formula and methods we have mastered.

However, there are times when a simpler solution can be done if we are able to see the logical side to the maths problem assigned.

Let me show an example.

Question:
2^x = 2⁴, find the value of x.

Solution: (mathematically)
Taking "log" on both sides, ==> x log 2 = 4 log 2 ==> x = 4 (log 2) / (log 2) = 4

Solution: (logically)
Comparing the values of their power, we get x = 4, since their base is the same (=2).
No working is needed!

Thus, maths does not actually just train us to do things systematically, it allows us to have a bit of mental freedom. This freedom is done in terms of the small little "twists" that make use of visual comparison or logical thinking (comparison).

Interesting approach to maths learning, right?
So many ways, mathematically and non-mathematically.
But best is the stretch to our mind to develop it to see things in many angles.

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