CONVERTING EXPONENTIAL TO LOGARITHMIC FORM

To convert logarithmic form to exponential form, we follow the procedure shown below.

Write the following equalities in exponential form.

Problem 1 :

log₃ 81 = 4

Solution :

Given logarithmic form :

log₃ 81 = 4

log_a m = x ó m = a^x

Exponential form :

81 = 3⁴

Problem 2 :

log₇ 7 = 1

Solution :

Given logarithmic form:

log₇ 7 = 1

log_a m = x ó m = a^x

Exponential form:

7 = 7¹

Problem 3 :

log_1/2 1/8 = 3

Solution :

Given logarithmic form:

log_1/2 1/8 = 3

log_a m = x ó m = a^x

Exponential form:

1/8 = (1/2)³

Problem 4 :

log₃ 1 = 0

Solution :

Given logarithmic form:

log₃ 1 = 0

log_a m = x ó m = a^x

Exponential form:

1 = 3⁰

Problem 5 :

log₄ 1/64 = -3

Solution :

Given logarithmic form:

log₄ 1/64 = -3

log_a m = x ó m = a^x

Exponential form:

1/64 = 4^-3

Problem 6 :

log₆ 1/36 = -2

Solution :

Given logarithmic form:

log₆ 1/36 = -2

log_a m = x ó m = a^x

Exponential form:

1/36 = 6^-2

Problem 7 :

log_x y = z

Solution :

Given logarithmic form:

log_x y = z

log_a m = x ó m = a^x

Exponential form:

y = x^z

Problem 8 :

log_m n = 1/2

Solution :

Given logarithmic form:

log_m n = 1/2

log_a m = x ó m = a^x

Exponential form:

n = m^1/2

n = √m