The approximate value of [tex]log_4128[/tex] is 3.5.
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to produce a number x is therefore the logarithm of a number x to the base b. For instance, since 1000 = 10^3, log10 of 1000 is 3, or log10 = 3.
Given: log 128≈ 2.1 and log 4≈ 0.6
We have to find the approximate value of [tex]log_4128[/tex].
We know that,
[tex]log_ba = \frac{loga}{logb}[/tex]
Here,
[tex]log_4128 = \frac{log128}{log4}[/tex]
Plug the values of log 128 and log 4
⇒ [tex]log_4128 = \frac{log128}{log4} = \frac{2.1}{0.6} = 3.5[/tex]
Hence, the approximate value of [tex]log_4128[/tex] is 3.5.
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