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Answer :
To write the equation [tex]\(5^4 = 625\)[/tex] in logarithmic form, we can use the following relationship between exponents and logarithms:
The logarithmic form of an equation [tex]\(a^b = c\)[/tex] is given by [tex]\(\log_a c = b\)[/tex].
In our case, we have:
- The base [tex]\(a\)[/tex] is 5.
- The exponent [tex]\(b\)[/tex] is 4.
- The result [tex]\(c\)[/tex] is 625.
So, the corresponding logarithmic form of [tex]\(5^4 = 625\)[/tex] is:
[tex]\[
\log_5 625 = 4
\][/tex]
Now, let's match this with the options given:
A. [tex]\(\log_4 625 = 5\)[/tex] is incorrect because the base should be 5, not 4.
B. [tex]\(\log_5 4 = 625\)[/tex] is incorrect because it swaps the exponent and the result.
C. [tex]\(\log_4 5 = 625\)[/tex] is incorrect because both the base and the expression inside the logarithm are incorrect.
D. [tex]\(\log_5 625 = 4\)[/tex] is correct because it correctly reflects the relationship where 5 raised to the power of 4 equals 625.
Therefore, the correct option is D. [tex]\(\log_5 625 = 4\)[/tex].
The logarithmic form of an equation [tex]\(a^b = c\)[/tex] is given by [tex]\(\log_a c = b\)[/tex].
In our case, we have:
- The base [tex]\(a\)[/tex] is 5.
- The exponent [tex]\(b\)[/tex] is 4.
- The result [tex]\(c\)[/tex] is 625.
So, the corresponding logarithmic form of [tex]\(5^4 = 625\)[/tex] is:
[tex]\[
\log_5 625 = 4
\][/tex]
Now, let's match this with the options given:
A. [tex]\(\log_4 625 = 5\)[/tex] is incorrect because the base should be 5, not 4.
B. [tex]\(\log_5 4 = 625\)[/tex] is incorrect because it swaps the exponent and the result.
C. [tex]\(\log_4 5 = 625\)[/tex] is incorrect because both the base and the expression inside the logarithm are incorrect.
D. [tex]\(\log_5 625 = 4\)[/tex] is correct because it correctly reflects the relationship where 5 raised to the power of 4 equals 625.
Therefore, the correct option is D. [tex]\(\log_5 625 = 4\)[/tex].
Thank you for reading the article Write the equation tex 5 4 625 tex in logarithmic form A tex log 4 625 5 tex B tex log 5 4 625 tex. 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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