2^(3-6х)>1

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вопрос

To solve the inequality, we first simplify the expression 2^(3-6x).

2^(3-6x) = 2^3 2^(-6x) = 8 1/(2^6x) = 8/(64^x)

Now the inequality becomes:

8/(64^x) > 1

This can be rewritten as:

8 > 64^x

Taking the square root of both sides, we get:

2^(3/x) > 8

Simplifying further, we get:

2^(3/x) > 2^3

Therefore, to satisfy the inequality, we must have:

3/x > 3

Dividing by 3 on both sides, we get:

x < 1

Therefore, the solution to the inequality 2^(3-6x) > 1 is x < 1.