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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] using the given values [tex]\(\log 128 \approx 2.1\)[/tex] and [tex]\(\log 4 \approx 0.6\)[/tex], we can use the change of base formula. This formula states:

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

Here, we need to determine [tex]\(\log_4 128\)[/tex]. Using the given values:

1. [tex]\(\log 128 \approx 2.1\)[/tex]
2. [tex]\(\log 4 \approx 0.6\)[/tex]

According to the formula:

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

Now, we perform the division:

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

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

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