Question

Log8 ( 7-6x)< 1/3 решите пожалуйста

Answer 1

7-6х<8 в степени1/3 
7-6х<2
-6х<2-7
-6х<-5
6х>5
Ответ х>5/6 

Answer 2

Solving the Inequality Log8(7-6x) < 1/3

To solve the inequality Log8(7-6x) < 1/3, we can follow these steps:

1. Isolate the Logarithmic Expression: - First, isolate the logarithmic expression by moving the constant to the other side of the inequality.

2. Convert to Exponential Form: - Once the logarithmic expression is isolated, convert it to exponential form to solve for the variable.

3. Solve for x: - After converting to exponential form, solve for the variable x.

Let's proceed with these steps.

Step 1: Isolate the Logarithmic Expression

To isolate the logarithmic expression Log8(7-6x), we can subtract 1/3 from both sides of the inequality:

Log8(7-6x) < 1/3 Log8(7-6x) - 1/3 < 0

Step 2: Convert to Exponential Form

The inequality Log8(7-6x) - 1/3 < 0 can be rewritten in exponential form as:

8^(1/3) < 7-6x

Step 3: Solve for x

Now, we can solve for x:

8^(1/3) < 7-6x 8^(1/3) - 7 < -6x (8^(1/3) - 7)/(-6) > x

So, the solution for the inequality Log8(7-6x) < 1/3 is: x > (8^(1/3) - 7)/(-6)

Therefore, the solution to the inequality is x > (8^(1/3) - 7)/(-6).

I hope this helps! If you have further questions or need additional assistance, feel free to ask.