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Rewrite the expression below in logarithmic form:

[tex]2^7 = 128[/tex]

A. [tex]\log_{128} 7 = 2[/tex]
B. [tex]\log_2 7 = 128[/tex]
C. [tex]\log_2 128 = 7[/tex]
D. [tex]\log_7 128 = 2[/tex]

Answer :

To rewrite the expression [tex]\(2^7 = 128\)[/tex] in logarithmic form, you need to remember the basic definition of logarithms:

If [tex]\(b^x = y\)[/tex], then [tex]\(\log_b y = x\)[/tex].

Let's apply this to the given expression:

1. Identify the base, the power (exponent), and the result:
- Base ([tex]\(b\)[/tex]) = 2
- Exponent ([tex]\(x\)[/tex]) = 7
- Result ([tex]\(y\)[/tex]) = 128

2. Using these values in the logarithmic form [tex]\(\log_b y = x\)[/tex], we substitute:
- [tex]\(\log_2 128 = 7\)[/tex]

Now let's match this with the options provided:

A. [tex]\(\log_{128} 7 = 2\)[/tex] — This is not correct.
B. [tex]\(\log_2 7 = 128\)[/tex] — This is not correct.
C. [tex]\(\log_2 128 = 7\)[/tex] — This matches what we derived.
D. [tex]\(\log_7 128 = 2\)[/tex] — This is not correct.

Thus, the correct answer is Option C: [tex]\(\log_2 128 = 7\)[/tex].

Thanks for taking the time to read Rewrite the expression below in logarithmic form tex 2 7 128 tex A tex log 128 7 2 tex B tex log 2 7 128. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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