Simple Way to Master Indices Maths Question

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Have you seen many mistakes like the below?


Question 1:
3^x = 27

Solution:
3^x = 3⁴ ===> x = 4

Question 2:
9^x = 3³

Solution:
3^3x = 3³ ===> 3x = 3 ===> x = 1

Why the error?

A simple explanation is that the maths learner is not familiar with the basic multiplication of repeated numbers.

3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49

2 x 2 x 2 = 8
3 x 3 x 3 = 27

2 x 2 x 2 x 2 = 16

etc.....

Once you have mastered this basic repeated multiplications, you can rest assure that indices question will not be there to haunt you.

How about solving "x" in this 9^{x + 1} + 2(3^x) - 3 = 0 ?

I bet that if you understood the above criteria of learning indices, the equation can be easily solved for x (using quadratic formula as a hint).

All complex things start off with simple things.
Do you agree this applies to maths?

:D