# How do you solve #(9)^(2k) = (3^5)^k#?

k = 0

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To solve the equation (9)^(2k) = (3^5)^k, we use the property of exponents that states (a^b)^c = a^(b*c).

Thus, we have:

(9)^(2k) = (3^5)^k => 9^(2k) = 3^(5k)

Since 9 is equal to 3^2, we substitute this into the equation:

(3^2)^(2k) = 3^(5k) => 3^(2*2k) = 3^(5k)

Now, using the property that if a^b = a^c, then b = c, we equate the exponents:

2*2k = 5k => 4k = 5k

Now, subtract 4k from both sides:

4k - 4k = 5k - 4k => 0 = k

Therefore, k = 0.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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