Question

Решить уравнение (2/3)^x • (9/8)^x=27/64​

Answer 1

Ответ:

$( \frac{2}{3} \times \frac{9}{8} ) {}^{x} = ( \frac{3}{4} ) {}^{3} \\ ( \frac{3}{4} ) {}^{x} = ( \frac{3}{4} ) {}^{3} \\ x = 3$

Answer 2

Відповідь:

Покрокове пояснення:

Answer 3

To solve the equation $(2/3)^x \cdot (9/8)^x = 27/64$, we can use the properties of exponents and algebraic manipulations. The goal is to get the variable $x$ on one side of the equation. Let's proceed step-by-step:

Step 1: Express all the fractions with common bases. We can rewrite $27/64$ as $(3/4)^3$ and $(9/8)^x$ as $(3/2)^x$:

$(2/3)^x \cdot (9/8)^x = (2/3)^x \cdot (3/2)^x = (2 \cdot 3 / 3 \cdot 2)^x = 1^x = 1$.

Step 2: We are left with the equation $1 = 1$, which is true for any value of $x$. This means that the original equation is an identity, and $x$ can take any real value.

Conclusion: The solution to the equation $(2/3)^x \cdot (9/8)^x = 27/64$ is $x \in \mathbb{R}$ (all real numbers).