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Answer :
To solve the problem of rewriting the logarithmic equation [tex]\(\log_5 625 = 4\)[/tex] in exponential form, let's break it down step-by-step:
1. Understanding Logarithms: A logarithmic expression [tex]\(\log_b a = c\)[/tex] means that the base [tex]\(b\)[/tex] raised to the power of [tex]\(c\)[/tex] equals [tex]\(a\)[/tex]. In other words, if you know the logarithm of a number, you can express it using exponents.
2. Identify the Components: In the provided problem, the base [tex]\(b\)[/tex] is 5, the number [tex]\(a\)[/tex] is 625, and the logarithm of [tex]\(a\)[/tex] base [tex]\(b\)[/tex] is 4. So we have:
[tex]\[
\log_5 625 = 4
\][/tex]
3. Convert to Exponential Form: According to the properties of logarithms:
[tex]\[
b^c = a
\][/tex]
Therefore, using the given values:
[tex]\[
5^4 = 625
\][/tex]
4. Choose the Correct Option: Compare the exponential form [tex]\(5^4 = 625\)[/tex] with the given options:
- Option A: [tex]\(4^5 = 625\)[/tex]
- Option B: [tex]\(5^4 = 625\)[/tex]
- Option C: [tex]\(4^5 = 1024\)[/tex]
- Option D: [tex]\(5^5 = 625\)[/tex]
The correct expression that matches [tex]\(5^4 = 625\)[/tex] is option B.
Therefore, the correct answer is B. [tex]\(5^4 = 625\)[/tex].
1. Understanding Logarithms: A logarithmic expression [tex]\(\log_b a = c\)[/tex] means that the base [tex]\(b\)[/tex] raised to the power of [tex]\(c\)[/tex] equals [tex]\(a\)[/tex]. In other words, if you know the logarithm of a number, you can express it using exponents.
2. Identify the Components: In the provided problem, the base [tex]\(b\)[/tex] is 5, the number [tex]\(a\)[/tex] is 625, and the logarithm of [tex]\(a\)[/tex] base [tex]\(b\)[/tex] is 4. So we have:
[tex]\[
\log_5 625 = 4
\][/tex]
3. Convert to Exponential Form: According to the properties of logarithms:
[tex]\[
b^c = a
\][/tex]
Therefore, using the given values:
[tex]\[
5^4 = 625
\][/tex]
4. Choose the Correct Option: Compare the exponential form [tex]\(5^4 = 625\)[/tex] with the given options:
- Option A: [tex]\(4^5 = 625\)[/tex]
- Option B: [tex]\(5^4 = 625\)[/tex]
- Option C: [tex]\(4^5 = 1024\)[/tex]
- Option D: [tex]\(5^5 = 625\)[/tex]
The correct expression that matches [tex]\(5^4 = 625\)[/tex] is option B.
Therefore, the correct answer is B. [tex]\(5^4 = 625\)[/tex].
Thank you for reading the article Write the equation tex log 5 625 4 tex in exponential form A tex 4 5 625 tex B tex 5 4 625 tex C. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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