How To Solve Exponential Equations

Exponential equations? What are they?
They are simply equations written in the indices form xⁿ = Y.

By looking at their simple form, we can deduce that their solution will not deviate much from simplicity also.

Lets look at a few examples.

Ex 1: Solve 2^x = 16

We change the 16 to 2⁴. This allows us to compare using the mathematical logic that when the base(2) is the same, the power of the base must be the same. 2^x = 2⁴.
Therefore x = 4 (Answer).

NOTE: How about doing something like 2^x = 15? This case we need Logarithm !

Ex 2: Solving the exponential equation 2^2k - 3(2^k) + 2 = 0.

This is slightly challenging in that the exponential equation is of the quadratic form.


Maths Tips: Let the 2^k be u. And 2^2k be u². This simplifies the outlook of the exponential equation without changing its meaning.

The new modified question becomes u² - 3u +2 = 0. Is this simpler to solve? Must be!


Moving on....

Using factorisation, we get (u - 1)(u -2) = 0.
Which means (u - 1) = 0 or (u - 2) = 0.
Therefore u = 1 or u = 2. Replacing the u = 2^k back to u,
2^k = 1= 2⁰ or 2^k = 2
Answer: k = 0 or k = 1.

From the above examples, they showed that with proper planning and understanding, solving exponential equations can be simple and fun.

Therefore strive to understand the principles of the topics, and all will be fine. :)

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