Question

Помогите пожалуйста, алгебру вообще не знаю. 1) Log2 (x-3) =2 2) log4 (2x-1) = log4 (3x-3)

Answer 1

1.log2(4)=2=>x=7
2.(2x-1) =(3x-3)=>-x=-2=>x=2

Answer 2

Solving the Equations

To solve the given equations, we will use the properties of logarithms. Let's solve each equation step by step:

Equation 1: ``` log2(x-3) = 2 ```

To eliminate the logarithm, we can rewrite the equation in exponential form: ``` 2^(log2(x-3)) = 2^2 ```

Simplifying further: ``` x - 3 = 4 ```

Adding 3 to both sides of the equation: ``` x = 7 ```

Therefore, the solution to Equation 1 is x = 7.

Equation 2: ``` log4(2x-1) = log4(3x-3) ```

Since the bases of the logarithms are the same, we can equate the arguments: ``` 2x - 1 = 3x - 3 ```

Subtracting 2x from both sides of the equation: ``` -x - 1 = -3 ```

Adding 1 to both sides of the equation: ``` -x = -2 ```

Multiplying both sides of the equation by -1 (to isolate x): ``` x = 2 ```

Therefore, the solution to Equation 2 is x = 2.

Summary

The solutions to the given equations are: - Equation 1: x = 7 - Equation 2: x = 2

Please let me know if you need any further assistance!