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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 for logarithms.
The change of base formula states that:
[tex]\[
\log_b a = \frac{\log a}{\log b}
\][/tex]
In this problem, we want to find [tex]\(\log_4 128\)[/tex]. Using the change of base formula, we substitute [tex]\(a = 128\)[/tex] and [tex]\(b = 4\)[/tex]:
[tex]\[
\log_4 128 = \frac{\log 128}{\log 4}
\][/tex]
Using the provided values:
[tex]\(\log 128 \approx 2.1\)[/tex]
[tex]\(\log 4 \approx 0.6\)[/tex]
We substitute these values into the formula:
[tex]\[
\log_4 128 \approx \frac{2.1}{0.6}
\][/tex]
Now we perform the division:
[tex]\[
\frac{2.1}{0.6} = 3.5
\][/tex]
Therefore, the approximate value of [tex]\(\log_4 128\)[/tex] is:
[tex]\[
\log_4 128 \approx 3.5
\][/tex]
The change of base formula states that:
[tex]\[
\log_b a = \frac{\log a}{\log b}
\][/tex]
In this problem, we want to find [tex]\(\log_4 128\)[/tex]. Using the change of base formula, we substitute [tex]\(a = 128\)[/tex] and [tex]\(b = 4\)[/tex]:
[tex]\[
\log_4 128 = \frac{\log 128}{\log 4}
\][/tex]
Using the provided values:
[tex]\(\log 128 \approx 2.1\)[/tex]
[tex]\(\log 4 \approx 0.6\)[/tex]
We substitute these values into the formula:
[tex]\[
\log_4 128 \approx \frac{2.1}{0.6}
\][/tex]
Now we perform the division:
[tex]\[
\frac{2.1}{0.6} = 3.5
\][/tex]
Therefore, the approximate value of [tex]\(\log_4 128\)[/tex] is:
[tex]\[
\log_4 128 \approx 3.5
\][/tex]
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