EXPONENTIAL FORM TO LOGARITHMIC FORM

Write the following equalities in logarithmic form.

Problem 1 :

8² = 64

Solution :

Given exponential form :

8² = 64

 xy = k ó y = logx k

Logarithmic form :

log8 64 = 2

Problem 2 :

103 = 10000

Solution :

Given exponential form :

103 = 10000

xy = k ó y = logx k

Logarithmic form :

 log10 10000 = 3

Problem 3 :

4-2 = 1/16

Solution :

Given exponential form :

4-2 = 1/16

xy = k ó y = logx k

Logarithmic form :

 log4 (1/16) = -2

Problem 4 :

1/81 = 3-4

Solution :

Given exponential form :

3-4 = 1/81

xy = k ó y = logx k

Logarithmic form :

 log3 (1/81) = -4

Problem 5 :

(1/2)-5 = 32

Solution :

Given exponential form :

(1/2)-5 = 32

xy = k ó y = logx k

Logarithmic form :

 log1/2 32 = -5

Problem 6 :

(1/3)-3 = 27

Solution :

Given exponential form :

(1/3)-3 = 27

xy = k ó y = logx k

Logarithmic form :

 log1/3 27 = -3

Problem 7 :

x2x = y

Solution :

Given exponential form :

x2z = y

xy = k ó y = logx k

Logarithmic form :

 logx y = 2z

Problem 8 :

√x = y

Solution :

Given exponential form :

√x = y

Take square on both sides.

(x)1/2 = y

xy = k ó y = logx k

Logarithmic form :

 logx y = 1/2

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