Question

3+2log2(x-7)=log2(2x+1) развернутый ответ​

Answer 1

Ответ:

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Объяснение:

Answer 2

Solving the Equation 3 + 2log2(x-7) = log2(2x+1)

To solve the equation 3 + 2log2(x-7) = log2(2x+1), we can follow these steps:

1. Isolate the Logarithmic Term: First, isolate the logarithmic term on one side of the equation.

2. Use Properties of Logarithms: Apply the properties of logarithms to simplify the equation.

3. Solve for x: Once the equation is simplified, solve for the variable x.

Let's proceed with solving the equation step by step.

Step 1: Isolate the Logarithmic Term

We start by isolating the logarithmic term 2log2(x-7) on one side of the equation.

Step 2: Apply Properties of Logarithms

We can use the property of logarithms that states log(a) + log(b) = log(ab) to simplify the equation.

Step 3: Solve for x

After simplifying the equation, we can solve for the variable x.

Let's proceed with the solution.

Solution:

1. Isolate the Logarithmic Term: Subtract 3 from both sides of the equation to isolate the logarithmic term: 2log2(x-7) = log2(2x+1) - 3

2. Apply Properties of Logarithms: We can use the property log(a) - log(b) = log(a/b) to simplify the equation: log2((x-7)^2) = log2(2x+1) - 3

3. Solve for x: Since the bases of the logarithms are the same, we can equate the expressions inside the logarithms: (x-7)^2 = 2x + 1)

Now, we can solve for x by expanding and rearranging the equation: x^2 - 14x + 49 = 2x + 1 x^2 - 16x + 48 = 0

We can solve this quadratic equation to find the values of x.

This is the detailed solution for the given equation. If you need further assistance or clarification, feel free to ask!