Question

Log2(x-6)=log2(2x-4)​

Answer 1

Log2(x-6)=log2(2x-4)
{x-6>0 x>6
{2x-4>0 x>2

x-6=2x-4
x-2x=6-4
-x=2
x=2 - корень не подходит по ОДЗ
Ответ: нет корней

Answer 2

To solve the equation log2(x - 6) = log2(2x - 4), we can use the logarithmic property that states:

log_a(b) = log_a(c) if and only if b = c.

So, in this case, we can set the expressions inside the logarithms equal to each other:

x - 6 = 2x - 4

Now, let's solve for x:

Step 1: Move all x terms to one side of the equation.

x - 2x = -4 + 6

Step 2: Combine like terms.

-x = 2

Step 3: Isolate x by multiplying both sides by -1.

x = -2

So, the solution to the equation is x = -2. However, we need to verify if this solution is valid. Since the original equation contains logarithms, the argument inside the logarithms must be positive:

1. For log2(x - 6) to be valid, x - 6 > 0 -2 - 6 > 0 -8 > 0 [This is false]

2. For log2(2x - 4) to be valid, 2x - 4 > 0 2(-2) - 4 > 0 -4 - 4 > 0 -8 > 0 [This is false]

Since both arguments inside the logarithms are not positive, the equation log2(x - 6) = log2(2x - 4) has no valid solutions.