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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[/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, which allows us to write logarithms in any base using common logarithms (base 10 in this instance). The formula is:

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

We are given the values [tex]\(\log 128 \approx 2.1\)[/tex] and [tex]\(\log 4 \approx 0.6\)[/tex]. Using these, we can calculate:

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

Substitute the given values into the formula:

[tex]\[
\log_4 128 \approx \frac{2.1}{0.6}
\][/tex]

Now, divide 2.1 by 0.6:

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

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

[tex]\[
\boxed{3.5}
\][/tex]

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