(√2) в x+2 степени =1/2

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вопрос

To solve this equation, we first need to isolate the variable x.

Starting with the given equation:

(√2)^(x+2) = 1/2

We can rewrite the left side using the property of exponents:

2^(1/2)^(x+2) = 1/2

Now, we simplify it further by multiplying the exponents:

2^(x/2 + 1) = 1/2

Now, we can rewrite the right side as a power of 2:

2^(-1) = 1/2

Therefore, our equation becomes:

2^(x/2 + 1) = 2^(-1)

Since the bases are the same, we can equate the exponents:

x/2 + 1 = -1

Now, we can solve for x:

x/2 = -2

x = -4

Therefore, the solution to the equation (√2)^(x+2) = 1/2 is x = -4.