EXPONENTIAL FORM TO LOGARITHMIC FORM

Write the following equalities in logarithmic form.

Problem 1 :

8² = 64

Solution :

Given exponential form :

8² = 64

 x^y = k ó y = log_x k

Logarithmic form :

log₈ 64 = 2

Problem 2 :

10³ = 10000

Solution :

Given exponential form :

10³ = 10000

x^y = k ó y = log_x k

Logarithmic form :

 log₁₀ 10000 = 3

Problem 3 :

4^-2 = 1/16

Solution :

Given exponential form :

4^-2 = 1/16

x^y = k ó y = log_x k

Logarithmic form :

 log₄ (1/16) = -2

Problem 4 :

1/81 = 3^-4

Solution :

Given exponential form :

3^-4 = 1/81

x^y = k ó y = log_x k

Logarithmic form :

 log₃ (1/81) = -4

Problem 5 :

(1/2)^-5 = 32

Solution :

Given exponential form :

(1/2)^-5 = 32

x^y = k ó y = log_x k

Logarithmic form :

 log_1/2 32 = -5

Problem 6 :

(1/3)^-3 = 27

Solution :

Given exponential form :

(1/3)^-3 = 27

x^y = k ó y = log_x k

Logarithmic form :

 log_1/3 27 = -3

Problem 7 :

x^2x = y

Solution :

Given exponential form :

x^2z = y

x^y = k ó y = log_x k

Logarithmic form :

 log_x y = 2z

Problem 8 :

√x = y

Solution :

Given exponential form :

√x = y

Take square on both sides.

(x)^1/2 = y

x^y = k ó y = log_x k

Logarithmic form :

 log_x y = 1/2