Select The Correct Answer.What Is This Equation Rewritten In Logarithmic Form? 9 X = 3 9^x=3 9 X = 3 A. Log ⁡ 9 3 = X \log_9 3 = X Lo G 9 ​ 3 = X B. Log ⁡ X 3 = 9 \log_x 3 = 9 Lo G X ​ 3 = 9 C. Log ⁡ 3 9 = X \log_3 9 = X Lo G 3 ​ 9 = X D. Log ⁡ 3 X = 9 \log_3 X = 9 Lo G 3 ​ X = 9

Introduction

Logarithmic equations are a fundamental concept in mathematics, and understanding how to rewrite them is crucial for solving various mathematical problems. In this article, we will focus on rewriting the equation $9^x=3$ in logarithmic form and explore the different options available.

What is Logarithmic Form?

Logarithmic form is a way of expressing an equation in terms of logarithms. It is a powerful tool for solving equations and is widely used in various fields, including mathematics, science, and engineering. The logarithmic form of an equation is typically written as $\log_b a = c$, where $b$ is the base of the logarithm, $a$ is the argument, and $c$ is the result.

Rewriting the Equation in Logarithmic Form

To rewrite the equation $9^x=3$ in logarithmic form, we need to use the definition of logarithms. The logarithmic form of an equation is given by:

$$\log_b a = c \iff b^c = a$$

Using this definition, we can rewrite the equation $9^x=3$ as:

$$\log_9 3 = x$$

This is because $9^x$ is equal to $3$, and the logarithmic form of this equation is $\log_9 3 = x$.

Analyzing the Options

Now that we have rewritten the equation in logarithmic form, let's analyze the options available:

• Option A: $\log_9 3 = x$
• Option B: $\log_x 3 = 9$
• Option C: $\log_3 9 = x$
• Option D: $\log_3 x = 9$

Option A: $\log_9 3 = x$

As we have already seen, the correct answer is $\log_9 3 = x$. This is because $9^x$ is equal to $3$, and the logarithmic form of this equation is $\log_9 3 = x$.

Option B: $\log_x 3 = 9$

This option is incorrect because the base of the logarithm is $x$, not $9$. The correct base of the logarithm is $9$, not $x$.

Option C: $\log_3 9 = x$

This option is incorrect because the argument of the logarithm is $9$, not $3$. The correct argument of the logarithm is $3$, not $9$.

Option D: $\log_3 x = 9$

This option is incorrect because the result of the logarithm is $9$, not $x$. The correct result of the logarithm is $x$, not $9$.

Conclusion

In conclusion, the correct answer is $\log_9 3 = x$. This is because $9^x$ is equal to $3$, and the logarithmic form of this equation is $\log_9 3 = x$. We have analyzed the options available and have shown that options B, C, and D are incorrect.

Common Mistakes to Avoid

When rewriting equations in logarithmic form, there are several common mistakes to avoid:

• Incorrect base: Make sure to use the correct base of the logarithm. In this case, the base is $9$, not $x$.
• Incorrect argument: Make sure to use the correct argument of the logarithm. In this case, the argument is $3$, not $9$.
• Incorrect result: Make sure to use the correct result of the logarithm. In this case, the result is $x$, not $9$.

Practice Problems

To practice rewriting equations in logarithmic form, try the following problems:

• Rewrite the equation $4^x=16$ in logarithmic form.
• Rewrite the equation $2^x=8$ in logarithmic form.
• Rewrite the equation $5^x=25$ in logarithmic form.

Solutions

• The equation $4^x=16$ can be rewritten in logarithmic form as $\log_4 16 = x$.
• The equation $2^x=8$ can be rewritten in logarithmic form as $\log_2 8 = x$.
• The equation $5^x=25$ can be rewritten in logarithmic form as $\log_5 25 = x$.

Conclusion

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Introduction

Logarithmic form is a powerful tool for solving equations and is widely used in various fields, including mathematics, science, and engineering. In this article, we will provide a Q&A guide to help you understand logarithmic form and how to apply it to solve equations.

Q: What is logarithmic form?

A: Logarithmic form is a way of expressing an equation in terms of logarithms. It is a powerful tool for solving equations and is widely used in various fields, including mathematics, science, and engineering.

Q: How do I rewrite an equation in logarithmic form?

A: To rewrite an equation in logarithmic form, you need to use the definition of logarithms. The logarithmic form of an equation is given by:

$$\log_b a = c \iff b^c = a$$

Using this definition, you can rewrite the equation $9^x=3$ as:

$$\log_9 3 = x$$

Q: What is the base of the logarithm?

A: The base of the logarithm is the number that is being raised to a power. In the equation $9^x=3$, the base of the logarithm is $9$.

Q: What is the argument of the logarithm?

A: The argument of the logarithm is the number that is being raised to a power. In the equation $9^x=3$, the argument of the logarithm is $3$.

Q: What is the result of the logarithm?

A: The result of the logarithm is the exponent that is being raised to a power. In the equation $9^x=3$, the result of the logarithm is $x$.

Q: How do I solve an equation in logarithmic form?

A: To solve an equation in logarithmic form, you need to use the definition of logarithms. The equation $\log_9 3 = x$ can be solved by raising the base of the logarithm to the power of the result:

$$9^x = 3$$

This equation can be solved by using logarithmic properties or by using algebraic methods.

Q: What are some common mistakes to avoid when rewriting equations in logarithmic form?

A: Some common mistakes to avoid when rewriting equations in logarithmic form include:

• Incorrect base: Make sure to use the correct base of the logarithm.
• Incorrect argument: Make sure to use the correct argument of the logarithm.
• Incorrect result: Make sure to use the correct result of the logarithm.

Q: How do I practice rewriting equations in logarithmic form?

A: To practice rewriting equations in logarithmic form, try the following problems:

• Rewrite the equation $4^x=16$ in logarithmic form.
• Rewrite the equation $2^x=8$ in logarithmic form.
• Rewrite the equation $5^x=25$ in logarithmic form.

Solutions

• The equation $4^x=16$ can be rewritten in logarithmic form as $\log_4 16 = x$.
• The equation $2^x=8$ can be rewritten in logarithmic form as $\log_2 8 = x$.
• The equation $5^x=25$ can be rewritten in logarithmic form as $\log_5 25 = x$.

Conclusion

In conclusion, logarithmic form is a powerful tool for solving equations and is widely used in various fields, including mathematics, science, and engineering. By understanding how to rewrite equations in logarithmic form, you can solve various mathematical problems and gain a deeper understanding of the subject. We have provided a Q&A guide to help you understand logarithmic form and how to apply it to solve equations.