# How do you solve #3^{4x - 4} = 9^{2x + 8}#?

Invalid equation. There is no solution.

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To solve the equation (3^{4x - 4} = 9^{2x + 8}), you can use the property that (9) can be expressed as (3^2).

So, rewrite (9) as (3^2) and then apply properties of exponents to simplify the equation.

[3^{4x - 4} = (3^2)^{2x + 8}]

Using the power of a power property, simplify the expression on the right side:

[(3^2)^{2x + 8} = 3^{2(2x + 8)}]

[= 3^{4x + 16}]

Now, the equation becomes:

[3^{4x - 4} = 3^{4x + 16}]

Since the bases are the same, the exponents must be equal:

[4x - 4 = 4x + 16]

Subtract (4x) from both sides:

[-4 = 16]

However, this equation leads to a contradiction. There is no value of (x) that satisfies the original equation. Therefore, the solution to (3^{4x - 4} = 9^{2x + 8}) is that there are no real solutions.

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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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