Solving Index expression in Quadratic form

In maths, the solving of indices questions and its quadratic counterparts are a common practice.

Depending on how you approach the solving, you may encounter a tough journey or a smooth-flowing one.

There are, however, simple tools and concepts that can be applied, in order to have fun solving them.

Here you go....

First, let's us take an example.

Example:
(2^x)² + 3(2^x) - 4 = 0

To solve this type of quadratic (index) equation, you have to take note of the common mistake in mis-interpreting the second term above.

This is the "3(2^x)" term. Refer to this link for explanation on the mistake.

Next, apply the concept of using "let" to the given equation.

This is needed to simplify the mathematical expression visually. Otherwise, it may look intimidating.

To learn about the power of using "Let", click here.

With the above 2 basic steps adhered to, you are ready to move forward into a relax solving environment to handle the given equation with ease.

Simplified equation: (After letting y = 2^x)

==> y² +3y -4 = 0

Applying next, the quadratic formula method, you can see that a = 1, b= 3 and c = -4.

Solving it for y, you will get 2 values shown below. ( Click here to learn how to make use of quadractic formula to solve.)

==> y = (-3 + 5)/2 = 1 and y = (-3-5)/2 = -4

After which, solve for x.
This y is related to x by the "letting" operation you have did in the first place, that is, y = 2^x.

y = 1: y = 2^x ==> 2^x = 1 = 2⁰ ==> x = 0 (Answer), logical comparison.

The other answer of y = -4 will not yield any valid real answer for x here.
( Why? --- see my next post).

So, you have done the solution very easily and without hiccups if you have understood the basic concept. If you have reviewed the working here, you will notice that there is nothing complex with all the steps.

Maths can be solved through a series of mind-blowing steps. But the reverse can also be true. It is up to you to define and choose the desire path.

Do not despair initially, as you need experience to manage this selection of strategy. How to achieve this experience? Simply practice and practice.

:-) ***