Question

Log1/3x>1 ; log1/3x<-1 ; log1/3x>-1 ; log1/3x<1

Answer 1

Решение на фото!

______________________________
удачи))

Answer 2

To solve the inequalities involving logarithms, we need to apply logarithmic rules and properties. Let's solve each inequality step by step:

1. log(1/3)x > 1:

To solve this inequality, we can use the property of logarithms that states: If log_b(x) > y, then b^y < x.

In our case, we have: log(1/3)x > 1

Using the property mentioned above: 1/3^1 < x

Simplify: 1/3 < x

2. log(1/3)x < -1:

Similarly, we'll use the property of logarithms: If log_b(x) < y, then b^y > x.

In our case, we have: log(1/3)x < -1

Using the property mentioned above: 1/3^(-1) > x

Simplify: 3 > x

3. log(1/3)x > -1:

Applying the property: 1/3^(-1) < x

Simplify: 3 < x

4. log(1/3)x < 1:

Using the property: 1/3^1 > x

Simplify: 1/3 > x

Summary of the solutions:

1. x > 1/3
2. x < 3
3. x > 3
4. x < 1/3

However, please note that when dealing with logarithmic inequalities, we need to ensure that the argument of the logarithm is positive. In this case, the argument of the logarithm (1/3)x should be greater than 0. So, we need to consider the valid interval for x as the intersection of the solutions to the inequalities and the domain of the logarithmic function, which is x > 0.

Therefore, the valid solution is:

1/3 < x < 3