Question

(5/3)^(3*x-8)<(25/9)^(x-3)

Answer 1

Данный ответ представлен фотографией.

Answer 2

To solve the inequality $(5/3)^{3x-8} < (25/9)^{x-3}$, we can start by working on the exponents and simplifying the terms. Let's break down the steps:

1. Rewrite $\frac{5}{3}$ and $\frac{25}{9}$ as powers of the same base: $\left(\frac{5}{3}\right)^{3x-8} < \left(\frac{5^2}{3^2}\right)^{x-3}$

2. Simplify the fractions inside the parentheses: $\left(\frac{5}{3}\right)^{3x-8} < \left(\frac{5}{3}\right)^{2(x-3)}$

3. Apply the property of exponents $(a^m)^n = a^{mn}$: $\left(\frac{5}{3}\right)^{3x-8} < \left(\frac{5}{3}\right)^{2x-6}$

4. Now we can compare the exponents: $3x-8 < 2x-6$

5. Subtract $2x$ from both sides: $x-8 < -6$

6. Add 8 to both sides: $x < 2$

So, the solution to the inequality is $x < 2$.