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  • Solving Logarithmic Equations

Example 5.4.1:

Solve the following equations:

(i) log (2x +1) – log (3x – 2) = 1 
(ii) log8x – 4log8x = 2
(iii) log x + log (x + 3) = 1 
(iv) log x – log (2x – 1) = 1  

Solution:

(i) log (2x + 1) – log (3x – 2) = 1 

⇒ \( \scriptsize \log \normalsize \frac{2x + 1}{3x – 2} = \scriptsize 1\) 

change to index form

⇒  \( \normalsize \frac{2x + 1}{3x – 2} = \scriptsize 10^1 \) 

cross multiply

⇒ 2x + 1 = 10(3x – 2)

2x + 1 = 30x – 20  

collect like terms

28x = 21

x = \( \frac{21}{28} \)

x = \( \frac{3}{4} \)

(ii) log8x – 4log8x = 2

 

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