 ## 4.2.2(a) Example 1 (Change of Base of Logarithms)

Example 1Find the value of the following.(a) log 4 8 (b) log 125 5 (c) log 81 27 (d) log 16 64

## 4.2.2 Change of Base of Logarithms

Change of Base of Logarithms     log a b= log c b log c a          and       log a b= 1 log b a       Example: Find the value of the following: a. log 25 100 b. log 3 0.45 Answer: (a)   log 25 100= log 10 100 log 10 25 = log 10 10 2 … Read more

## 4.2.1(c) Example 3 (Laws of Logarithms)

Example 3 Given that log 7 4 = 0.712   and log 7 5 = 0.827  , evaluate the following. (a) log 7 20 (b) log 7 1 1 4 (c) log 7 0.8 (d) log 7 28 (e) log 7 140 (f) log 7 100 (g) log 7 0.25 (h) log 7 35 64

## 4.2.1(b) Example 2 (Laws of Logarithms)

Example 2 Find the value of the following. (a) log 2 7 + log 2 12 − log 2 21 (b) 3 log 10 5 + 2 log 10 2 − log 10 5 (c) 2 log 10 3 − log 10 3 + log 10 3 1 3 (d) log 3 3 p + … Read more

## 4.2.1(a) Example 1 (Laws of Logarithms)

Example 1 Express the following in term of log a x   and log a y  . (a) log a 3 x (b) log a x 5 (c) log a y 5 (d) log a x y 3 (e) log a x 2 y (f) log a y a 2 x 3 Law of Logarithms

## 4.2.1 Laws of Logarithms

4.2a Laws of Logarithms   Law 1:   log a x y = log a x + log a y   Example:   log 5 25 x = log 5 25 + log 5 x   Beware!!   log a x + log a y ≠ log a ( x + y )      Law 2:   log a ( x y ) … Read more

## 4.2(a) Example 1 (Logarithms)

Example 1 Find the value of each of the following :(a) log 2 64 (b) log 3 1 (c) log 5 5 (d) log 1 2 4 (e) log 8 0.25

## 4.2 Logarithms

4.2 Logarithms N = a x           ⇔           log a N = x log a N = x is called the logarithmic form and N = a x is the index or exponential form. Note: The logarithm of a negative number is not defined. log in … Read more

## 4.1.2 Indices and Laws of Indices (Part 2)

4.1 Indices and Laws of Indices (Part 2) (C) Fractional Indices    a 1 n  is a  n th root of  a .    a 1 n = a n    a m n  is a  n th root of  a m .    a m n = a m n Example 1: Find the value of the followings: (a) 81 1 … Read more