Question

1/2 * (9/25) ^ x = 27/250​

Answer 1

$\displaystyle\bf\\\frac{1}{2} \cdot\Big(\frac{9}{25} \Big)^{x} =\frac{27}{250} \\\\\\\frac{1}{2} \cdot\Big(\frac{9}{25} \Big)^{x}\cdot 2 =\frac{27}{250}\cdot 2\\\\\\\Big(\frac{9}{25} \Big)^{x} =\frac{27}{125} \\\\\\\Big(\frac{3}{5} \Big)^{2x} =\Big(\frac{3}{5} \Big)^{3} \\\\\\2x=3\\\\\boxed{x=1,5}$

Answer 2

To solve for the variable "x" in the equation:

(1/2) * (9/25)^x = 27/250

You can follow these steps:

1. Start by isolating the term with the variable "x" on one side of the equation. In this case, we want to get rid of the (1/2) on the left side. To do this, you can multiply both sides of the equation by 2:

2 * (1/2) * (9/25)^x = 2 * 27/250

This simplifies to:

(9/25)^x = (2 * 27)/250

2. Next, simplify the right side:

(9/25)^x = 54/250

3. Reduce the fraction on the right side by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(9/25)^x = 27/125

4. To isolate the variable "x," you can take the natural logarithm (ln) of both sides of the equation. This will allow you to use logarithm properties to solve for "x."

ln((9/25)^x) = ln(27/125)

Using the property ln(a^b) = b * ln(a):

x * ln(9/25) = ln(27/125)

5. Now, solve for "x" by dividing both sides by ln(9/25):

x = ln(27/125) / ln(9/25)

6. Calculate the value of "x" using a calculator:

x ≈ 0.5434

So, the approximate value of "x" is 0.5434.