Sample complete logarithm questions with tips

Logarithmic mathematics



 Calculate the numerical value of the following statements.


1. log 4 16 + log 3 9 − log 100

2. 2 log 3 √3 + 3 log 0.1 + log 4 √2

3. 3log3 4 + 53 log5 3

4. log 6 12 + log 6 3
1
5. 22 log2 4−log2 8 + 3log3 9+log33

6. 𝑒 ln 3 + ln 𝑒 5 + ln √𝑒


 If log 2 = 𝑎 , log 3 = 𝑏 , log 5 = 𝑐 , calculate the following values
in terms of a, b, c


1
7. log √2 − log 27 + log
5
25 5
8 . log 5 + log √2
9 √2




 Solve the following equations


9. 3𝑥+2 = 27
2 −1
10. 5𝑥 = 25𝑥+1
11. 42𝑥−1 = 83𝑥

, Logarithmic mathematics




12. log 5(2𝑥) + 10 = 2
13. log(𝑥 2 + 3𝑥) = 2 log 𝑥 − 1
14. log 3(𝑥 2 − 4) − log 3 (4𝑥 − 7) = 0
15. log 2(𝑥 + 3) + log 2 (𝑥 + 2) = 1
16. log(𝑥 − 3) + log(𝑥 + 3) = log 5
17. log(𝑥 2 + 4𝑥 + 3) − log(𝑥 − 2) = log(𝑥 + 5)




 Solve the following inequalities


2 −2𝑥
18. 3𝑥 > 3𝑥
2 +4𝑥
19. 0.4𝑥+4 < 0.4𝑥

20. log 5 3𝑥 < 1

21. log( 𝑥 2 − 3) < 0

22. log 0.2 (𝑥 + 4) < log 0.2 (𝑥 2 − 2)

23. log(𝑥 2 + 4) < log 5𝑥