5 в степени -x больше 625

To solve the inequality 5^(-x) > 625, we need to find the value of x that makes the inequality true.

First, let's rewrite 625 as a power of 5: 625 = 5^4

So, the inequality becomes: 5^(-x) > 5^4

Using the property of exponents that states a^(-n) = 1/a^n, we can rewrite the inequality as: 1/5^x > 5^4

Next, we need to eliminate the fraction. We can do this by multiplying both sides of the inequality by 5^x: 1 > 5^4 * 5^x

Using the property of exponents that states a^m * a^n = a^(m+n), we can simplify the right side of the inequality: 1 > 5^(4+x)

To make the inequality true, we need the base to be the same on both sides. So, we can rewrite 1 as a power of 5: 1 = 5^0

Now, we have: 5^0 > 5^(4+x)

Since the bases are the same, we can equate the exponents: 0 > 4 + x

To solve for x, we can subtract 4 from both sides of the inequality: -4 > x

Therefore, the solution to the inequality 5^(-x) > 625 is x < -4.