Question

2log[2/5]x+5log[5]x+2=0

Answer 1

Ответ:

x=$\sqrt[7]{200}$/10

Пошаговое объяснение:

Answer 2

To solve the equation 2log(2/5)x + 5log(5)x + 2 = 0, you can use logarithmic properties and algebraic techniques. Here's how you can do it step by step:

1. Start by isolating the logarithmic terms on one side of the equation. Subtract 2 from both sides:

2log(2/5)x + 5log(5)x = -2

2. Now, you can use logarithmic properties to simplify the equation. Remember that log(a) + log(b) = log(ab), and log(a^n) = n*log(a):

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

3. Calculate the values inside the logarithms:

log(4/25) + log(3125)x = -2

4. Use the logarithmic property log(a) + log(b) = log(ab) to combine the logarithms:

log((4/25) * 3125x) = -2

5. Simplify the right side of the equation:

log((4/25) * 3125x) = -2

6. Now, you can remove the logarithm by exponentiating both sides of the equation. Since the base of the logarithm is 10 (common logarithm), we'll use 10 as the base:

10^log((4/25) * 3125x) = 10^(-2)

7. On the left side, 10^log(y) = y, so:

(4/25) * 3125x = 1/100

8. Multiply both sides by 100 to eliminate the fraction:

(4/25) * 3125x * 100 = 1

9. Simplify:

(4/25) * 312500x = 1

10. Now, divide both sides by (4/25) * 312500 to solve for x:

x = 1 / [(4/25) * 312500]

11. Calculate the value of x:

x = 1 / (4/25) * 312500 x = 25/4 * 312500 x = 1953125

So, the solution to the equation is x = 1953125.