Question

3^(2x-1) - 8/3^(2x-1) - 1 = -1 в скобках степени 20 баллов

Answer 1

Делаем замену
Пусть 3^(2x-1)=t,t>0
Тогда t-8/t -1 +1=0
t-8/t=0
t^2-8t=0
t(t-8)=0
t=0 и t=8
Делаем обратную замену
3^(2x-1) =0 : нет решений
3^(2x-1)= 8 : 2x-1=log по основанию 3 от 8

Answer 2

To solve the equation $3^{2x-1} - \frac{8}{3^{2x-1}} - 1 = -1$, we can simplify it first and then find the value of $x$. Let's proceed with the steps:

Step 1: Get rid of the fraction by multiplying the entire equation by $3^{2x-1}$:

$3^{2x-1} \cdot 3^{2x-1} - 8 - 3^{2x-1} = -3^{2x-1}$

Step 2: Combine the terms on the left side:

$3^{4x-2} - 8 - 3^{2x-1} = -3^{2x-1}$

Step 3: Move all terms to one side of the equation:

$3^{4x-2} - 3^{2x-1} + 3^{2x-1} + 8 = 0$

Step 4: Combine like terms:

$3^{4x-2} + 8 = 0$

Step 5: Subtract 8 from both sides:

$3^{4x-2} = -8$

At this point, it seems there might be a mistake in the original equation because the left side is always positive (since $3^{4x-2}$ is a positive number), whereas the right side is negative. It means there is no real value of $x$ that can satisfy this equation. The equation does not have any real solutions.

If you have made a typo in the original equation or meant something else, please provide the correct equation so that I can help you further.