In the following equation, what are possible values for c and d?
4^c · 4^d = 4^9
c =
d =
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In the following equation, what are possible values for c and d?
4^c · 4^d = 4^9
c =
d =
To solve the equation ( 4^c cdot 4^d = 4^9 ), we can use the properties of exponents.
When we multiply two expressions with the same base, we can add their exponents:
[
4^c cdot 4^d = 4^{c+d}
]
This means we can rewrite the equation as:
[
4^{c+d} = 4^9
]
Since the bases are the same, we can set the exponents equal to each other:
[
c + d = 9
]
Now, (c) and (d) can be any pair of numbers that add up to 9. For example:
– If (c = 0), then (d = 9).
– If (c = 1), then (d = 8).
– If (c = 4), then (d = 5).
– If (c = 9), then (d = 0).
So, there are many possible values for (c) and (d) as long as they satisfy the equation (c + d = 9).
In summary:
– (c) can be any value, and (d) will be (9 – c).
– (d) can be any value, and (c) will be (9 – d