Question

2^х-1 – 3^х = 3^х+1 – 2^х+2​

Answer 1

Пошаговое объяснение:

2^х-1-3^х = 3^х+1-2^х+2

2^х-3^х-3^х+2^х = 1+2

-2^х=3

Х=2

Answer 2

To solve the equation $2^{x-1} - 3^x = 3^{x+1} - 2^{x+2}$, we'll first simplify it by using exponent rules and then attempt to isolate the variable $x$.

Let's work on simplifying the equation step by step:

1. Start by expressing both sides with a common base, either $2$ or $3$. We'll use $3$ because it's the larger base:

   $3^x = (3^{x-1} - 2^{x+2}) + 3^x$

2. Now, move one of the $3^x$ terms to the left side by subtracting it from both sides:

   $3^x - 3^x = 3^{x-1} - 2^{x+2}$

3. The left side simplifies to $0$:

   $0 = 3^{x-1} - 2^{x+2}$

4. Now, let's further simplify the right side by writing $2^{x+2}$ as $2^x \cdot 2^2 = 4 \cdot 2^x$:

   $0 = 3^{x-1} - 4 \cdot 2^x$

5. Next, let's move the $4 \cdot 2^x$ term to the left side by adding it to both sides:

   $4 \cdot 2^x = 3^{x-1}$

6. Now, we can rewrite $4$ as $2^2$:

   $2^2 \cdot 2^x = 3^{x-1}$

7. Use the rule that $a^m \cdot a^n = a^{m+n}$:

   $2^{2+x} = 3^{x-1}$

8. Since both sides have the same base, we can equate the exponents:

   $2+x = x-1$

9. Now, isolate $x$ on one side:

   $2+x-x = -1$

   $2 = -1$

This equation $2 = -1$ is not true for any value of $x$, so there is no real solution to the original equation $2^{x-1} - 3^x = 3^{x+1} - 2^{x+2}$. It appears there might be a mistake in the original equation or the way it was transcribed. Please double-check the equation or provide additional context if needed.