Question

3^{x+1}*[tex]9^{x-1/2} = ∛3. Решите плис

Answer 1

X+1+2x-1=1/3

3x=1/3

x=1/3*1/3=1/9

Answer 2

Solving the Equation

To solve the equation 3^(x+1) * 9^(x-1/2) = ∛3, we can simplify the equation and then solve for the value of x.

Let's break down the steps:

Step 1: Simplify the equation We can simplify the equation by using the properties of exponents and radicals.

First, let's rewrite 9 as 3^2 since 9 is equal to 3 raised to the power of 2.

The equation becomes: 3^(x+1) * (3^2)^(x-1/2) = ∛3

Using the property of exponents, we can simplify the equation further: 3^(x+1) * 3^(2(x-1/2)) = ∛3

Next, we can simplify the exponent 2(x-1/2): 2(x-1/2) = 2x - 1

The equation becomes: 3^(x+1) * 3^(2x - 1) = ∛3

Step 2: Combine the exponents To combine the exponents, we can use the property of exponents that states: a^m * a^n = a^(m+n).

Applying this property, we can rewrite the equation as: 3^(x+1 + 2x - 1) = ∛3

Simplifying the exponents, we get: 3^(3x) = ∛3

Step 3: Solve for x To solve for x, we need to isolate the variable x on one side of the equation.

Taking the cube root of both sides of the equation, we get: 3x = ∛(∛3)

Simplifying the cube root of ∛3, we get: 3x = ∛(3^(1/3))

Now, we can solve for x by dividing both sides of the equation by 3: x = (∛(3^(1/3))) / 3

Please note that without the exact value of ∛(3^(1/3)), it is not possible to provide a numerical solution for x. However, the above equation represents the solution in terms of the given expression.

I hope this helps! Let me know if you have any further questions.