Question

5^(2x-1)=0,4 × 2^(2x-1)​

Answer 1

$5^{2x-1} =0,4*2^{2x-1}\\\\\frac{5^{2x-1} }{2^{2x-1} }=\frac{0,4*2^{2x-1} }{2^{2x-1}};2^{2x-1}\neq0\\\\(\frac{5}{2})^{2x-1}=\frac{2}{5}\\\\(\frac{5}{2})^{2x-1}=(\frac{5}{2})^{-1}\\\\2x-1=-1\\\\2x=0\\\\x=0$

Answer 2

${5}^{2x - 1} = 0.4 \times {2}^{2x - 1 } \\ 1 = \frac{2}{5} \times {2}^{2x - 1 } \div {5}^{2x - 1} \\ 1 = { \frac{2}{5} }^{2x} \\ 2x = 0 \\ x = 0$

Answer 3

To solve the equation 5^(2x-1) = 0.4 * 2^(2x-1), we can use logarithms. Let's begin:

Step 1: Take the logarithm of both sides of the equation. We can use any base for the logarithm, but let's use the natural logarithm (ln) for this example: ln(5^(2x-1)) = ln(0.4 * 2^(2x-1))

Step 2: Apply the logarithmic property that states ln(a^b) = b * ln(a): (2x-1) * ln(5) = ln(0.4 * 2^(2x-1))

Step 3: Expand the right side of the equation using the logarithmic property ln(a * b) = ln(a) + ln(b): (2x-1) * ln(5) = ln(0.4) + ln(2^(2x-1))

Step 4: Simplify the right side further: (2x-1) * ln(5) = ln(0.4) + (2x-1) * ln(2)

Step 5: Distribute (2x-1) on the left side of the equation: 2x * ln(5) - ln(5) = ln(0.4) + (2x-1) * ln(2)

Step 6: Move all terms containing x to one side and the constant terms to the other side: 2x * ln(5) - 2x * ln(2) = ln(5) + ln(0.4) - ln(2)

Step 7: Factor out x: x * (2 * ln(5) - 2 * ln(2)) = ln(5) + ln(0.4) - ln(2)

Step 8: Divide both sides by (2 * ln(5) - 2 * ln(2)): x = (ln(5) + ln(0.4) - ln(2)) / (2 * ln(5) - 2 * ln(2))

Step 9: Use a calculator to evaluate the right side: x ≈ 0.122

Therefore, the approximate solution to the equation 5^(2x-1) = 0.4 * 2^(2x-1) is x ≈ 0.122.