Question

Log2log√5(x-1)<1 ^-^ пжж​

Answer 1

Ответ:

x от(1;6)

Объяснение:

Answer 2

It seems like you're asking about an inequality involving logarithms. Let's break down the expression and solve the inequality:

1. The given inequality is: log2(log(√5, x - 1)) < 1

2. First, simplify the inner logarithm: log(√5, x - 1) = log(x - 1) / log(√5) = log(x - 1) / (1/2 * log(5))

3. Now, rewrite the original inequality with this expression: log2(log(x - 1) / (1/2 * log(5))) < 1

4. To get rid of the logarithms and simplify further, you can rewrite it as an exponential equation: 2^(log(x - 1) / (1/2 * log(5))) < 2^1

5. Since 2^1 is just 2, you have: 2^(log(x - 1) / (1/2 * log(5))) < 2

6. Now, simplify further by getting rid of the base 2: 2^(log(x - 1) / (1/2 * log(5))) can be rewritten as (x - 1)^(1/(1/2 * log(5))) = (x - 1)^(2 * log(5))

7. So, the inequality becomes: (x - 1)^(2 * log(5)) < 2

8. To solve for x, you can take the square root of both sides: √((x - 1)^(2 * log(5))) < √2

9. This simplifies to: |x - 1|^(2 * log(5)) < √2

10. Now, raise both sides to the power of (1 / (2 * log(5))) to eliminate the exponent: |x - 1| < (√2)^(1 / (2 * log(5)))

11. Finally, simplify: |x - 1| < 5^(1 / (2 * log(5)))

This is the solution to the given inequality. Depending on the exact values of the logarithms involved, you may need to approximate the right side of the inequality to find a numeric solution for x.