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].
[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].