Question

0,5^2x-1<8 решите плисе неравенство

Answer 1

0,5 ^ 2x - 1 < 8 
2 ^ ( - 2x + 1 ) > 2 ^ 3 
- 2x + 1 > 3 
2x < - 2 
x < - 1 
( - ∞ ; - 1 )

Answer 2

The given inequality is:

0.5^(2x-1) < 8

First, we can simplify the left-hand side by using the fact that (a^b)^c = a^(bc):

0.5^(2x-1) = (0.5^2)^(x-0.5) = 0.25^(x-0.5)

Substituting this expression back into the inequality, we get:

0.25^(x-0.5) < 8

Taking the logarithm of both sides with base 0.25, we obtain:

(x-0.5)log0.25 < log8

Dividing both sides by log0.25 (which is negative), we reverse the inequality:

x - 0.5 > log8 / log0.25

x > log8 / log0.25 + 0.5

Using a calculator, we can evaluate the right-hand side to be approximately 7.51. Therefore, the solution to the inequality is:

x > 7.51 + 0.5

x > 8.01