Answer :

To find the approximate value of [tex]\log_4 128[/tex], we can use the change of base formula in logarithms. The change of base formula states that for any positive numbers [tex]a, b[/tex], and [tex]c[/tex] (with [tex]a \neq 1, b \neq 1[/tex]), the logarithm [tex]\log_a b[/tex] can be calculated as:

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

In this case, to find [tex]\log_4 128[/tex], we can use any logarithm base, but since we are given [tex]\log 128 \approx 2.1[/tex] and [tex]\log 4 \approx 0.6[/tex] (where the base is 10, which we assume due to convention unless specified otherwise), we will use base 10.

Applying the change of base formula, we have:

[tex]\log_4 128 = \frac{\log_{10} 128}{\log_{10} 4} = \frac{2.1}{0.6}[/tex]

By dividing these values, we calculate:

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

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

The process effectively changes the base of the logarithm to a base that we can easily compute using given values, allowing us to solve the problem accurately and simply.

Thanks for taking the time to read Use the values log 128 2 1 and log 4 0 6 to find the approximate value of log₄ 128 log₄ 128. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada