Question

((sqrt(5)) ^ (x - 10))/(4 ^ (x - 10)) > (5sqrt(5))/64

Answer 1

Ответ:

(-∞;13)

Объяснение:

Answer 2

To solve the inequality, let's simplify the expressions on both sides:

((sqrt(5)) ^ (x - 10))/(4 ^ (x - 10)) > (5sqrt(5))/64

Let's simplify the left side first:

((sqrt(5)) ^ (x - 10))/(4 ^ (x - 10)) = (sqrt(5) / 4) ^ (x - 10)

Now our inequality becomes:

(sqrt(5) / 4) ^ (x - 10) > (5sqrt(5)) / 64

To make it easier to compare, let's convert the right side to the same base as the left side:

(sqrt(5) / 4) ^ (x - 10) > (sqrt(5) * sqrt(5) * sqrt(5)) / (4 * 4 * 4)

(sqrt(5) / 4) ^ (x - 10) > (5 * sqrt(5)) / 64

Now we can compare the exponents:

x - 10 > 5 / 64

Simplify further:

x > 10 + 5/64

x > 10.078125

Therefore, the solution to the inequality is x > 10.078125.