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Problem #29 · August 25, 2026
Powers and roots
If
5
x
5
3
=
5
7
\dfrac{5^{x}}{5^{3}} = 5^{7}
5
3
5
x
=
5
7
, find
x
x
x
.
A
4
4
4
B
21
21
21
C
✓
10
10
10
D
7
7
7
E
35
35
35
WORKED EXAMPLE
Solution
When dividing, subtract the exponents:
5
x
5
3
=
5
x
−
3
\dfrac{5^{x}}{5^{3}} = 5^{x-3}
5
3
5
x
=
5
x
−
3
. Thus,
5
x
−
3
=
5
7
5^{x-3} = 5^{7}
5
x
−
3
=
5
7
, which gives
x
−
3
=
7
x - 3 = 7
x
−
3
=
7
, so
x
=
10
x = 10
x
=
10
.
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