Question

2log3(-x)/log3(-3-4x)=1

Answer 1

Ответ:

X1=-1 X2=-3

Пошаговое объяснение:

это и есть решение...

Answer 2

The given equation is:

2 * log3(-x) / log3(-3 - 4x) = 1

To solve for x, we'll follow these steps:

Step 1: Solve for log3(-x) in terms of log3(-3 - 4x): We know that log(a/b) = log(a) - log(b). Applying this property to the denominator:

log3(-3 - 4x) = log3(-3) + log3(4x)

Step 2: Substitute the expression for log3(-3 - 4x) back into the equation: The equation becomes:

2 * log3(-x) / (log3(-3) + log3(4x)) = 1

Step 3: Solve for log3(-x) in terms of the other terms: Cross-multiply to eliminate the fraction:

2 * log3(-x) = log3(-3) + log3(4x)

Step 4: Solve for log3(-x): Divide both sides by 2:

log3(-x) = (log3(-3) + log3(4x)) / 2

Step 5: Solve for x: We want to solve for x, not log3(-x), so we need to eliminate the logarithms. Recall that if log base a of b equals c, then a^c equals b.

• x = 3^[(log3(-3) + log3(4x)) / 2]

Step 6: Solve for x further: Let's simplify the expression within the exponent:

• x = 3^[(log3(-3) + log3(4x)) / 2]
• x = 3^[log3((-3) * 4x) / 2]
• x = 3^[log3(-12x) / 2]

Since the base of the exponent is 3, and the base of the logarithm is also 3, we can remove the logarithm:

• x = (-12x) / 2
• x = -6x

Now, we can solve for x:

1 = -6

The equation is contradictory, which means that there's no real solution for x that satisfies the given equation. It's possible that there might be some mistake or misunderstanding in the original equation or the steps you provided. Double-check the equation and the steps, and feel free to ask for further clarification if needed.