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Use the values [tex]\log 128 \approx 2.1[/tex] and [tex]\log 4 \approx 0.6[/tex] to find the approximate value of [tex]\log_4 128[/tex].

[tex]\log_4 128 \approx \qquad[/tex]

The solution is [tex]\square[/tex].

Answer :

To find the approximate value of [tex]\(\log_4 128\)[/tex], we can use the change of base formula. The change of base formula states that:

[tex]\[
\log_b a = \frac{\log_c a}{\log_c b}
\][/tex]

For this question, we want to find [tex]\(\log_4 128\)[/tex]. We can use the standard logarithm base (common logarithm, [tex]\(\log\)[/tex]) for our calculation. According to the given values, we have:

- [tex]\(\log 128 \approx 2.1\)[/tex]
- [tex]\(\log 4 \approx 0.6\)[/tex]

Using the change of base formula:

[tex]\[
\log_4 128 = \frac{\log 128}{\log 4} = \frac{2.1}{0.6}
\][/tex]

Now, perform the division:

[tex]\[
\frac{2.1}{0.6} = 3.5
\][/tex]

Therefore, the approximate value of [tex]\(\log_4 128\)[/tex] is [tex]\(3.5\)[/tex].

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