Question

find the value. give an approximation to four decimal places.
$log 373 + log 16$

8.6942

3.0966

16.4181

3.7758

question 24

find the average rate of change of the function from $x_1$ to $x_2$.
$f(x) = sqrt{2x}$ from $x_1 = 2$ to $x_2 = 8$

7

$-\frac{3}{10}$

$\frac{1}{3}$

2

Explanation:

First Question (Logarithm Problem)

Step1: Apply Logarithm Property

Use the property $\log a + \log b = \log(ab)$. So, $\log 373 + \log 16 = \log(373\times16)$.
Calculate $373\times16 = 5968$.

Step2: Calculate Logarithm

Assuming base 10 (common logarithm), calculate $\log(5968)$. Using a calculator, $\log(5968) \approx 3.7758$.

Second Question (Average Rate of Change)

Step1: Recall Average Rate Formula

The average rate of change of a function $f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$.

Step2: Find $f(x_1)$ and $f(x_2)$

Given $f(x)=\sqrt{2x}$, $x_1 = 2$, $x_2 = 8$.

• $f(2)=\sqrt{2\times2}=\sqrt{4}=2$.
• $f(8)=\sqrt{2\times8}=\sqrt{16}=4$.

Step3: Compute Average Rate

Substitute into the formula: $\frac{f(8)-f(2)}{8 - 2}=\frac{4 - 2}{6}=\frac{2}{6}=\frac{1}{3}$.

Answer:

3.7758