 ## 4.4 Equations Involving Logarithms

METHOD:For two logarithms of the same base, if log a m = log a n , then m = n .  Convert to index form, if log a m = n , then m = an. Example 1Solve the following equation:(a) log 3 2 + log 3 ( x + 5 ) = log 3 … Read more

## 4.3.5 Example 5 (Unequal Base – put log both side)

Example 5Solve each of the following.(a) 3 x + 1 = 7 (b) 2 ( 3 x ) = 5 (c) 2 x .3 x = 9 x − 4 (d) 5 x − 1 .3 x + 2 = 10

## 4.3.4 Example 4 (Index Equation – Substitution)

Example 4Solve each of the following.(a) 3 x − 1 + 3 x = 12 (b) 2 x + 2 x + 3 = 72 (c) 4 x + 1 + 2 2 x = 20

## 4.3.3 Example 3 (Solving Index Equation Simultaneously)

Example 3 (Solving index equation simultaneously)Solve the following simultaneous equations. 2 x .4 2 y = 8 3 x 9 y = 1 27

## 4.3.2 Example 2 (Index Equation – Equal Base)

Example 2Solve each of the following.(a) 27 ( 81 3 x ) = 1 (b) 81 n + 2 = 1 3 n 27 n − 1 (c) 8 x − 1 = 4 2 x + 3

## 4.3.1 Example 1 (Index Equation – Equal base)

Example 1Solve each of the following.(a) 16 x = 8 (b) 9 x .3 x − 1 = 81 (c) 5 n + 1 = 1 125 n − 1

## 4.3 Equations Involving Indices

METHOD: Comparison of indices or base If  the base are the same , when a x = a y , then x = y If  the index are the same , when a x = b x , then a = b Using common logarithm (If base and index are NOT the same) a x … Read more

## 4.2.2(d) Example 4 (Change of Base of Logarithms)

Example 4Given that log 2 3 = 1.585   and log 2 5 = 2.322  , evaluate the following. (a) log 8 15 (b) log 5 0.6 (c) log 15 30 (d) log 16 45 Solution:

## 4.2.2(b) Example 2 (Change of Base of Logarithms)

Example 2Given that log p 3 = h   and log p 5 = k  , express the following in term of h and or k. (a) log p 5 3 (b) log 15 75