Question

Log1/2(x+2)=1 как решить?

Answer 1

ОДЗ:x² - x - 2 > 0D = 1 + 8 = 9x₁ = (1-3)/2 = -1x₂ = (1+3)/2 = 2x∈(-∞; -1)U(2;+∞)

Answer 2

To solve the equation $\log_{\frac{1}{2}}(x+2) = 1$, we can follow these steps:

Step 1: Rewrite the equation in exponential form. Step 2: Solve for the value of $x$.

Step 1: Rewrite the equation in exponential form. In logarithmic form, the equation $\log_b(y) = x$ is equivalent to $b^x = y$. So, applying this to our equation:

$\log_{\frac{1}{2}}(x+2) = 1$ is equivalent to $\left(\frac{1}{2}\right)^1 = x+2$.

Step 2: Solve for the value of $x$. Now, we can solve for $x$:

$\frac{1}{2} = x+2$

To isolate $x$, subtract 2 from both sides:

$\frac{1}{2} - 2 = x$

$-\frac{3}{2} = x$

So, the solution for the equation is $x = -\frac{3}{2}$.