To convert logarithm to exponential form, we have to follow the steps given below.

Step 1 :

From the logarithmic function, move the base to the other side of the equal sign.

Step 2 :

We are allowed to move the base only and the quantity what we have after the equal sign will be written in the power.

Step 3 :

Using one of the properties of exponents we can continue solving it.

Step 4 :

Powers can be equated when we see same bases on both sides of the equal sign.

ax = ay

Then, x = y

Bases can be equated when we see same powers on both sides of the equal sign.

ax = bx

Then, a = b

Find the value of y.

Problem 1 :

log5 25 = y

Solution:

y = log5 25

Exponential form:

5y = 25

Writing 25 in exponential form, we get

5y = 52

Since bases are equal, we can equate the powers.

y = 2

Problem 2 :

log3 1 = y

Solution:

﻿log3 1 = y

Exponential form:

3y = 1

Anything to the power of 0 is 1.

3y = 30

Equating the powers, we get

y = 0

Problem 3 :

log16 4 = y

Solution:

log16 4 = y

y = log16 4

Exponential form:

16y = 4

Since 16 is the multiple of 4, we can write 16 in exponential form with the base 4.

(42)y = 4

42y = 41

Equating the power, we get

2y = 1

y = 1/2

Problem 4 :

Solution:

Exponential form:

Problem 5 :

log5 1 = y

Solution:

﻿log5 1 = y

Exponential form:

5y = 1

Anything to the power of 0 is 1.

5y = 50

y = 0

Problem 6 :

log2 8 = y

Solution:

﻿log2 8 = y

Exponential form:

2y = 8

Writing 8 in exponential form, we get

2y = 23

By equating the powers, we get

y = 3

Problem 7 :

Solution:

Exponential form:

Problem 8 :

Solution:

Exponential form:

Problem 9 :

logy 32 = 5

Solution:

logy 32 = 5

32 = y5

32 can be written in exponential form.

25 = y5

Since the powers are equal, we can equate the bases.

y = 2

Problem 10 :

Solution:

Problem 11 :

Solution:

Exponential form:

Problem 12 :

Solution:

Exponential form:

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