Dr. J's Maths.com
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are explained in simple terms.

Functions - Logarithmic functions - Log Laws.
Test Yourself 2.


 

Use the six laws of logarithms as outlined in the video to simplify/solve the following:

Log laws with numbers.

1. log2 48 - log2 3

 2.
  3. 4.
  5. 6.
  7. 8.
Log laws with pronumerals.

9. log3 81x - log3 9x

= log3 (81x/9x) = log3 9

=log3 32 = 2 log3 3 = 2

 10.
  11. 12.
  13.  
  15.  
  17.  
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  21.  
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  25. 26.
  27.
  28.
Substitution 29. Given log pq = 1.544 and
log qr = 1.113,

30.

(i) log 45 = log (9 × 5)

= 2 log 3 + log 5

= 2b + c

(ii) log (10/9) = log 10 - log 9

= log 2 + log 5 - 2log 3

= a + c - 2b

(iii)

(iv)

 

31.(i)

(ii)

32. (i)

(ii)

Equations 33. 34.
 

35.

36.
  37.

38.

 
 

39.

40.
  41. Solve log5 (4 - x) = 1 + 2 log5 x

42. 3log72 = log7x - log75.