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.
a^{x} = a^{y}
Then, x = y
Bases can be equated when we see same powers on both sides of the equal sign.
a^{x} = b^{x}
Then, a = b
Find the value of y.
Problem 1 :
log_{5} 25 = y
Solution:
y = log_{5} 25
Exponential form:
5^{y} = 25
Writing 25 in exponential form, we get
5^{y} = 5^{2}
Since bases are equal, we can equate the powers.
y = 2
Problem 2 :
log_{3} 1 = y
Solution:
log_{3} 1 = y
Exponential form:
3^{y} = 1
Anything to the power of 0 is 1.
3^{y} = 3^{0}
Equating the powers, we get
y = 0
Problem 3 :
log_{16} 4 = y
Solution:
log_{16} 4 = y
y = log_{16} 4
Exponential form:
16^{y} = 4
Since 16 is the multiple of 4, we can write 16 in exponential form with the base 4.
(4^{2})^{y} = 4
4^{2y} = 4^{1}
Equating the power, we get
2y = 1
y = 1/2
Problem 4 :
Solution:
Exponential form:
Problem 5 :
log_{5} 1 = y
Solution:
log_{5} 1 = y
Exponential form:
5^{y} = 1
Anything to the power of 0 is 1.
5^{y} = 5^{0}
y = 0
Problem 6 :
log_{2} 8 = y
Solution:
log_{2} 8 = y
Exponential form:
2^{y} = 8
Writing 8 in exponential form, we get
2^{y} = 2^{3}
By equating the powers, we get
y = 3
Problem 7 :
Solution:
Exponential form:
Problem 8 :
Solution:
Exponential form:
Problem 9 :
log_{y} 32 = 5
Solution:
log_{y} 32 = 5
32 = y^{5}
32 can be written in exponential form.
2^{5} = y^{5}
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:
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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