Question

Lg(x-1)^2=0 решите уравнение

Answer 1

$\lg (x-1)^2=0\\\\(x-1)^2=10^0\\x^2-2x+1=1\\x^2-2x=0\\x(x-2)=0\\x=0\\x=2$

Оба корня удовлетворяют ОДЗ,

Answer 2

To solve the equation $Lg(x-1)^2=0$, we can start by understanding the logarithmic function involved. The $Lg$ function typically refers to the logarithm with base 10, commonly denoted as $\log_{10}$.

Now, we can proceed with the solution:

1. Start with the given equation: $Lg(x-1)^2=0$.

2. Since the logarithm of a number is equal to zero only when the number itself is 1, we have $(x-1)^2=1$ from the equation $Lg(x-1)^2=0$.

3. Take the square root of both sides to eliminate the square: $x-1 = \pm 1$.

4. Solve for $x$ in each case: a) $x - 1 = 1$ Add 1 to both sides: $x = 1 + 1$ --> $x = 2$.

   b) $x - 1 = -1$ Add 1 to both sides: $x = -1 + 1$ --> $x = 0$.

So, the solutions to the equation $Lg(x-1)^2=0$ are $x = 2$ and $x = 0$.