Principles of Mathematics

Solving Exponential Equations

What is exponential equations?
It is simply an equation of the indices form xⁿ = Y.   Solving them is also simple!

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).

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 forward….
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, it shows that with proper planning and understanding, solving exponential equations can be simple and fun.

Article Submitted by: Lim Ee Hai
Article Source: http://www.limehai.com