Problem 1 :
Find the missing exponent.
Problem 2 :
Find the missing exponent.
Problem 3 :
Find the missing exponent.
Problem 4 :
Find the missing exponent.
Problem 5 :
Find the missing exponent.
Problem 6 :
Find the missing exponent.
Problem 7 :
Find the missing exponent.
Problem 8 :
Find the missing exponent.
Problem 1 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
25 = 5x
To get the same base on both sides, write 25 in terms of 5 using exponent.
52 = 5x
Equate the exponents.
2 = x
So, the missing exponent is 2.
Problem 2 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
8 = 2x
To get the same base on both sides, write 8 in terms of 2 using exponent.
23 = 2x
Equate the exponents.
3 = x
So, the missing exponent is 3.
Problem 3 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
100 = 10x
To get the same base on both sides, write 100 in terms of 10 using exponent.
102 = 10x
Equate the exponents.
2 = x
So, the missing exponent is 2.
Problem 4 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
27 = 3x
To get the same base on both sides, write 27 in terms of 3 using exponent.
33 = 3x
Equate the exponents.
3 = x
So, the missing exponent is 3.
Problem 5 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
1/169 = (1/13)x
Write 169 in terms of 13 using exponent.
1/132 = (1/13)x
13-2 = (13-1)x
13-2 = 13-x
Equate the exponents.
-2 = -x
Multiply each side by (-1).
2 = x
So, the missing exponent is 2.
Problem 6 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
14 = 14x
Already, we have the same on both sides.
141 = 14x
Equate the exponents.
1 = x
So, the missing exponent is 1.
Problem 7 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
64/81 = (8/9)x
Write 64 in terms 8 and 81 in terms of 9 using exponent.
82 / 92 = (8/9)x
(8/ 9)2 = (8/9)x
Equate the exponents.
2 = x
So, the missing exponent is 2.
Problem 8 :
Find the missing exponent.
Solution :
Let 'x' be the missing exponent.
Then,
32 = 2x
Write 32 in terms of 2 using exponent.
25 = 2x
Equate the exponents.
5 = x
So, the missing exponent is 5.
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