**Indices**

**Fractional Indices:**

**Law of Indices:**

**How to simplify algebraic expressions**

**Example 1:**

**Example 2:**

**Example 3: **

**Logarithms**

If then . So . For example, if , then , where index 4 becomes the logarithms and 2 as the base.

In general, , we call them as **common logarithms** (base 10). The [log] where you can find from calculator is the common logarithm.

**Example 4: **

Find the value of

*Answer: 1.2788 [Use Calculator to find the answer]*

**Example 5:**

Solve

*Answer: m = 0.0027 [Press (shift)(log)(-2.5686)]*

**Laws of Logarithms: **

`1) `

**Example 6:**

`2) `

**Example 7:**

`3) `

**Example 8: **

`4) `

**Example 9:**

`5) `

**Example 10:**

,

**Change the Base of Logarithm **

1)

2)

**Example 11: **

Evaluate

The following examples need to be solved using the Laws of Logarithms and change of base. So please remember the laws of logarithms and the change of the base of logarithms.

**Example 12:**

Find the value of

**Example 13: **

Simplify

**Solving Equation involving indices and logarithms**

a) Method 1: Expressing the equation to same base and compare the indices.

b) Method 2: Expressing the equation to same indices and compare the base.

c) Method 3: Using

d) Method 4: Expressing the equation as a single logarithms form to the same base

**About the Authors:**

Mr Low – A full time tutor from Malaysia, passionate about teaching Mathematics for PMR Maths, SPM Additional Maths, SPM Modern Maths and International School Maths included SAT,GCSE, Checkpoint, IGCSE syllabus.

Ms Tifeny – A full time tutor from Malaysia teaching Mathematics for SPM Additional Maths, STPM Maths and International School Maths included SAT,GCSE, Checkpoint, IGCSE syllabus, A-level, Pre-U and IB.