Question

Log0,2(x+4)=-1 решить

Answer 1

Ответ: х=1.

Пошаговое объяснение:

log₀,₂(x+4)=-1       ОДЗ: x+4>0      x>-4   ⇒   x∈(-4;+∞).

x+4=0,2⁻¹

x+4=(1/5)⁻¹

x+4=5

x=1 ∈ОДЗ.

Answer 2

To solve the equation $\log_{0.2}(x+4) = -1$, we need to rewrite it in exponential form. The logarithmic equation $\log_b(x) = y$ can be rewritten as an exponential equation $b^y = x$. Applying this to our equation:

$0.2^{-1} = x + 4$

Now, we can simplify the left-hand side:

$\frac{1}{0.2} = 5 = x + 4$

Now, isolate $x$ on one side of the equation:

$x = 5 - 4$

$x = 1$

So, the solution to the equation is $x = 1$.