LOGARITHM QUESTIONS WITH SOLUTIONS

Question 1 :

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

Solution :

y  =  b^x

log_by  =  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)

=  (3/2)  - (2/3)

=  (9 - 4)/6

=  5/6

Question 3 :

Solve for x : 

log₈x + log₄x + log₂x  =  11

Solution :

(1/log_x8) + (1/log_x4) + (1/log_x2)  =  11

(1/3log_x2) + (1/2log_x2) + (1/log_x2)  =  11

(1/log_x2)[(1/3) + (1/2) + 1]  =  11

(1/log_x2) (2 + 3 + 6)/6  =  11

(1/log_x2)(11/6)  =  11

(1/log_x2)  =  6

log_x2  =  1/6

2  =  x^1/6

2⁶  =  x

x  =  64

Question 4 :

Solve for x : 

log₄2^8x  =  2^log₂⁸

Solution :

(8x)log₄2  =  2^3log₂²

(8x)log₄2  =  8

log₄2  =  8/8x

log₄2  =  1/x

2  =  4^1/x

2^x  =  4

2^x  =  2²

x  =  2

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