LOGARITHM QUESTIONS WITH SOLUTIONS

Question 1 :

Let b > 0 and b ≠ 1. Express y = bx in logarithmic form. Also state the domain and range of the logarithmic function.

Solution :

y  =  bx

logby  =  x

Domain : (0, ∞)

Range : (-∞, ∞)

Question 2 :

Compute :

log927 − log279

Solution :

=  log927 - log279

=  log933 - log2732

=  3log93 - 2log273

=  3(1/log39)  - 2(1/log327)

=  3(1/2log33)  - 2(1/3log3)

=  (3/2)  - (2/3)

=  (9 - 4)/6

=  5/6

Question 3 :

Solve for x : 

log8x + log4x + log2x  =  11

Solution :

(1/logx8) + (1/logx4) + (1/logx2)  =  11

(1/3logx2) + (1/2logx2) + (1/logx2)  =  11

(1/logx2)[(1/3) + (1/2) + 1]  =  11

(1/logx2) (2 + 3 + 6)/6  =  11

(1/logx2)(11/6)  =  11

(1/logx2)  =  6

logx2  =  1/6

2  =  x1/6

26  =  x

x  =  64

Question 4 :

Solve for x : 

log428x  =  2log28

Solution :

(8x)log42  =  23log22

(8x)log42  =  8

log42  =  8/8x

log42  =  1/x

2  =  41/x

2x  =  4

2x  =  22

x  =  2

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