Question

(2/3)^(2x+3)=(27/8)^(x-1)

Answer 1

Ответ:

Пошаговое объяснение:

(2/3)^(2x+3)=((2/5)^-3)^(x-1)

(2/3)^(2x+3)=(2/5)^(-3x+3)

2x+3= -3x+3

2x+3x=3-3

5x=0

x=0

Answer 2

To solve the equation, we can use logarithms to eliminate the exponents. Let's go through the steps:

1. Start with the given equation: (2/3)^(2x+3) = (27/8)^(x-1).

2. Take the logarithm of both sides of the equation. We can use any logarithm base, but let's use the natural logarithm (ln) for this example: ln((2/3)^(2x+3)) = ln((27/8)^(x-1)).

3. Apply the power rule of logarithms, which states that log(a^b) = b * log(a), to simplify both sides of the equation: (2x + 3) * ln(2/3) = (x - 1) * ln(27/8).

4. Use logarithmic properties to simplify further: ln(2/3)^(2x+3) = ln((27/8)^(x-1)). (2x + 3) * ln(2/3) = (x - 1) * ln(27/8). ln(2/3) * (2x + 3) = ln(27/8) * (x - 1).

5. Divide both sides of the equation by ln(2/3) to isolate the x terms: 2x + 3 = (ln(27/8) * (x - 1)) / ln(2/3).

6. Simplify the expression on the right side: 2x + 3 = (ln(27/8) * x - ln(27/8)) / ln(2/3).

7. Multiply both sides of the equation by ln(2/3) to eliminate the denominator: ln(2/3) * (2x + 3) = ln(27/8) * x - ln(27/8).

8. Distribute ln(2/3) on the left side: (2x + 3) * ln(2/3) = ln(27/8) * x - ln(27/8).

9. Expand both sides of the equation: 2x * ln(2/3) + 3 * ln(2/3) = x * ln(27/8) - ln(27/8).

10. Group the x terms on one side and the constant terms on the other side: 2x * ln(2/3) - x * ln(27/8) = -3 * ln(2/3) - ln(27/8).

11. Factor out x on the left side: x * (2 * ln(2/3) - ln(27/8)) = -3 * ln(2/3) - ln(27/8).

12. Divide both sides by (2 * ln(2/3) - ln(27/8)) to solve for x: x = (-3 * ln(2/3) - ln(27/8)) / (2 * ln(2/3) - ln(27/8)).

This is the simplified solution for x based on the given equation.