Use The Equation $2,401 = 7^6 - 2x$.What Power Of 7 Is 2,401?A. 3 B. 4 C. 5

Introduction

In this article, we will delve into the world of mathematics and solve an equation that involves the power of 7. The equation is $2,401 = 7^6 - 2x$. Our goal is to find the value of x and determine the power of 7 that is equal to 2,401. This problem requires us to use algebraic manipulation and mathematical reasoning to arrive at the solution.

Understanding the Equation

The given equation is $2,401 = 7^6 - 2x$. To solve for x, we need to isolate the variable x on one side of the equation. We can start by adding 2x to both sides of the equation, which gives us:

$2,401 + 2x = 7^6$

Next, we can subtract 2,401 from both sides of the equation to get:

$2x = 7^6 - 2,401$

Now, we can divide both sides of the equation by 2 to solve for x:

$x = \frac{7^6 - 2,401}{2}$

Calculating the Value of x

To calculate the value of x, we need to evaluate the expression $7^6 - 2,401$. We can start by calculating the value of $7^6$:

$7^6 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 = 117,649$

Now, we can subtract 2,401 from the result:

$117,649 - 2,401 = 115,248$

Finally, we can divide the result by 2 to get the value of x:

$x = \frac{115,248}{2} = 57,624$

Determining the Power of 7

Now that we have the value of x, we can determine the power of 7 that is equal to 2,401. We can start by rewriting the equation as:

$2,401 = 7^6 - 2x$

Substituting the value of x that we calculated earlier, we get:

$2,401 = 7^6 - 2(57,624)$

Simplifying the equation, we get:

$2,401 = 7^6 - 115,248$

Now, we can add 115,248 to both sides of the equation to get:

$117,649 = 7^6$

This tells us that $7^6$ is equal to 117,649. However, we are looking for the power of 7 that is equal to 2,401. To find this, we can rewrite the equation as:

$2,401 = 7^x$

We can start by trying different values of x to see if we can find a match. Let's try x = 3:

$7^3 = 7 \times 7 \times 7 = 343$

This is not equal to 2,401, so we can try a higher value of x. Let's try x = 4:

$7^4 = 7 \times 7 \times 7 \times 7 = 2,401$

This is equal to 2,401, so we have found the power of 7 that is equal to 2,401.

Conclusion

In this article, we solved the equation $2,401 = 7^6 - 2x$ and determined the power of 7 that is equal to 2,401. We found that $7^4$ is equal to 2,401. This problem required us to use algebraic manipulation and mathematical reasoning to arrive at the solution. We hope that this article has provided a clear and concise explanation of how to solve this type of problem.

Final Answer

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Introduction

In our previous article, we solved the equation $2,401 = 7^6 - 2x$ and determined the power of 7 that is equal to 2,401. We found that $7^4$ is equal to 2,401. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on how to solve this type of problem.

Q&A

Q: What is the equation $2,401 = 7^6 - 2x$ trying to solve?

A: The equation $2,401 = 7^6 - 2x$ is trying to solve for the value of x. We need to isolate the variable x on one side of the equation to find its value.

Q: How do we solve for x in the equation $2,401 = 7^6 - 2x$?

A: To solve for x, we need to add 2x to both sides of the equation, which gives us $2,401 + 2x = 7^6$. Then, we can subtract 2,401 from both sides of the equation to get $2x = 7^6 - 2,401$. Finally, we can divide both sides of the equation by 2 to solve for x.

Q: What is the value of x in the equation $2,401 = 7^6 - 2x$?

A: To calculate the value of x, we need to evaluate the expression $7^6 - 2,401$. We can start by calculating the value of $7^6$, which is 117,649. Then, we can subtract 2,401 from the result to get 115,248. Finally, we can divide the result by 2 to get the value of x, which is 57,624.

Q: How do we determine the power of 7 that is equal to 2,401?

A: To determine the power of 7 that is equal to 2,401, we can rewrite the equation as $2,401 = 7^x$. We can start by trying different values of x to see if we can find a match. Let's try x = 3, which gives us $7^3 = 343$. This is not equal to 2,401, so we can try a higher value of x. Let's try x = 4, which gives us $7^4 = 2,401$. This is equal to 2,401, so we have found the power of 7 that is equal to 2,401.

Q: What is the final answer to the equation $2,401 = 7^6 - 2x$?

A: The final answer to the equation $2,401 = 7^6 - 2x$ is x = 57,624. However, the question is asking for the power of 7 that is equal to 2,401, which is $7^4$.

Q: Can you provide more examples of how to solve this type of problem?

A: Yes, here are a few more examples:

• $3,125 = 5^6 - 2x$
• $1,024 = 2^10 - 2x$
• $81 = 3^4 - 2x$

In each of these examples, we need to add 2x to both sides of the equation, subtract 2,401 from both sides of the equation, and then divide both sides of the equation by 2 to solve for x.

Q: What are some common mistakes to avoid when solving this type of problem?

A: Some common mistakes to avoid when solving this type of problem include:

• Not adding 2x to both sides of the equation
• Not subtracting 2,401 from both sides of the equation
• Not dividing both sides of the equation by 2 to solve for x
• Not trying different values of x to find a match

By avoiding these common mistakes, you can ensure that you are solving the equation correctly and finding the correct value of x.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on how to solve the equation $2,401 = 7^6 - 2x$. We hope that this article has been helpful in understanding how to solve this type of problem. If you have any further questions or need additional help, please don't hesitate to ask.