Class notes

Key topics covered in the Class:

• Law of Indices (Exponent Law)

• Exponential Function

LAST CLASS REVISION

Log- Inequality

• When solving log inequalities, the direction of the inequality sign depends on the base
a.

• If the base is greater than 1 ( 𝑎 > 1), the inequality sign stays the same. For example, if
𝑙𝑜𝑔𝑎 (𝑏) > 𝑐, then 𝑏 > 𝑎𝑐 . This is because the function is increasing.
• If the base is between 0 and 1 ( 0 < 𝑎 < 1), the sign reverses. For example, if
𝑙𝑜𝑔𝑎 (𝑏) > 𝑐, then 𝑏 < 𝑎𝑐 . This is because the function is decreasing.




LAW OF EXPONENT (INDICES)
• These are the basic rules for working with powers, such as 𝑎𝑚 ⋅ 𝑎𝑛 = 𝑎𝑚+𝑛
(multiplication) and(𝑎𝑚 )𝑛 = 𝑎𝑚𝑛 (power of a power).
1
• A negative exponent means taking the reciprocal, e.g., 𝑎−𝑚 = 𝑎𝑚 . A fractional exponent
𝑚
represents a root, e.g., 𝑎1/𝑚 = √𝑎.
• Any non-zero number raised to the power of zero equals 1 (𝑎0 = 1 for 𝑎 ≠ 0). However,
00 is not defined.

EXPONENTIAL FUNCTION
• An exponential function has the form𝑦 = 𝑎 𝑥 , where the base a is a positive constant not
equal to 1.