Mathematical statement 2x² - 7x - 6

For $\log 2445$:
Characteristic = 3 (since 2445 has 4 digits, $4-1=3$).
Mantissa for 24 under 4 is 0.3874. Mean difference for 5 is 9.
So, $\log 2445 = 3.3874 + 0.0009 = 3.3883$.

For $\log 0.106$:
Characteristic = $\bar{1}$ (since the first non-zero digit is in the first decimal place).
Mantissa for 10 under 6 is 0.0253.
So, $\log 0.106 = \bar{1}.0253$.

We will use 0.8045 for finding the antilog.

Antilog of 0.8045:
Look up 0.80 under 4, which gives 6.368.
The mean difference for 5 (in the row for 80) is 7.
So, antilog $0.8045 = 6.368 + 0.007 = 6.375$.
Since the characteristic of $\log s$ is 0 (from 0.8045), the decimal point is after the first digit.
So, $s = 6.375$.

$s \approx 6.4$ cm.
The length of one side of the cube is $\boxed{6.4 \text{ cm}}$.

16. The population of a small village in Turkana grows at a rate modeled using indices. If the initial population $P$ triples every 5 years, use laws of indices to find how long it takes for the population to reach 9 times its original size.

Let the initial population be $P_0$.
The population triples every 5 years.
After $t$ years, the population $P(t)$ can be expressed as:

We want to find the time $t$ when the population reaches 9 times its original size, i.e., $P(t) = 9P_0$.

Since the bases are the same, the exponents must be equal.

It takes $\boxed{10 \text{ years}}$ for the population to reach 9 times its original size.