Question

2 ^ (x + 2) = sqrt(0.5)

Answer 1

$\displaystyle\bf\\2^{x+2}=\sqrt{0,5} \\\\2^{x+2} =\sqrt{\frac{1}{2} } \\\\2^{x+2} =\sqrt{2^{-1} } \\\\2^{x+2} =2^{-\frac{1}{2} } \\\\2^{x+2} =2^{-0,5} \\\\x+2=-0,5\\\\\boxed{x=-2,5}$

Answer 2

Ответ:

x= -2,5

Объяснение:

$2^{(x + 2)} = \sqrt{0,5} \\\\2^x*2^2=\sqrt{\frac{1}{2} } \\2^x*2^2=\frac{1}{2} ^{\frac{1}{2}}\\2^x=2^{-\frac{1}{2}}:2^2\\2^x=2^{-\frac{1}{2}-2}\\2^x=2^{-\frac{5}{2}}\\x=-\frac{5}{2} \\x=-2,5$

Answer 3

To solve the equation 2^(x + 2) = sqrt(0.5), we need to isolate the variable x.

Let's break down the steps to solve the equation:

1. Take the logarithm of both sides of the equation to remove the exponent. log(2^(x + 2)) = log(sqrt(0.5))

2. Apply the logarithmic property log(a^b) = b * log(a). (x + 2) * log(2) = log(sqrt(0.5))

3. Simplify the logarithms. (x + 2) * log(2) = log(0.5^(1/2))

4. Simplify the right side of the equation. (x + 2) * log(2) = log(0.5^(1/2)) (x + 2) * log(2) = log(0.5^0.5) (x + 2) * log(2) = log(sqrt(0.5))

5. Since log(2) is a constant, let's denote it as a single variable, such as "k". k = log(2)

6. Rewrite the equation using the variable "k." (x + 2) * k = log(sqrt(0.5))

7. Solve for x by isolating it on one side of the equation. x + 2 = log(sqrt(0.5)) / k x = log(sqrt(0.5)) / k - 2

8. Substitute the value of k (log(2)) back into the equation. x = log(sqrt(0.5)) / log(2) - 2

Now you can calculate the numerical value of x using a calculator.