Question

Log^2 0,5 x-log0,5 x=6

Answer 1

 

ОДЗ: 

   







 -убывающая, 

поэтому                 

 

1) x<0          
                    
   
                 
      
          
   
     
при x<0   ответом будет (-2;-1]     

2) x>0          
        
    
      
             
     
          
 
при x>0 ответом будет [1;2)
Ответ:  

Answer 2

It appears you're trying to solve a logarithmic equation. The equation you've provided is:

log^2(0.5x) - log(0.5x) = 6

To solve this equation, you can use logarithm properties. First, let's simplify it by noticing that log^2(0.5x) can be rewritten as (log(0.5x))^2. So, the equation becomes:

(log(0.5x))^2 - log(0.5x) = 6

Now, let's make a substitution to simplify it further. Let y = log(0.5x). Then the equation becomes:

y^2 - y = 6

This is now a quadratic equation in terms of y. Let's solve it by factoring:

y^2 - y - 6 = 0

Now, factor the quadratic:

(y - 3)(y + 2) = 0

Set each factor equal to zero:

1. y - 3 = 0 y = 3

2. y + 2 = 0 y = -2

Now that we have two possible values for y, we need to find the corresponding values of x. Remember that we initially defined y as y = log(0.5x).

For y = 3:

log(0.5x) = 3

Now, exponentiate both sides to get rid of the logarithm:

0.5x = 10^3 0.5x = 1000

Multiply both sides by 2 to isolate x:

x = 2000

For y = -2:

log(0.5x) = -2

Again, exponentiate both sides:

0.5x = 10^(-2) 0.5x = 0.01

Now, multiply both sides by 2:

x = 0.02

So, there are two solutions to the equation:

x = 2000 and x = 0.02