Exponential equations

Let’s do a quick recap of what we learned about quadratic equations

Look at this example: Solve for y:

2y² + 12 = 8x -3

Step 1: Rewrite in standard form: 2y² -8x + 15 = 0 [8x becomes -8x inverse operation; 12 + 3 =15]

Step 2: Factorise: (2y -5)(2y -3) = 0

Step 3: Apply null factor law to solve for two roots: 2y = 5 OR 2y = 3

Step 4: Divide both sides by co-efficient: y = 5/2 OR y = 3/2

Exponential equations

Sometimes an equation has an exponent that is a variable e.g.:

3^x = 9

In this case we first need to get the bases of all the terms to be equal. Let’s try 3 as the likely base:

3^x = 3²

Now we can remove the bases and treat it as any other equation:

x=2

This can help us solve some complicated equations: 

16^x – 8^x /  2^x+8 =0

Make the bases the same:

2^4x – 2^3x/ 2^1x + 2³ = 0                  [When dividing we subtract exponents]

2^4x – 2^2x + 2³ = 0                           [Now remove bases and simplify]

2x + 3 = 0                                         [Solve]

x = -3/2

 Coming next: Simultaneous equations!