Question

question 31 (3 points)
\\(\log_{5}(125) =\\)
\\(\bigcirc 4\\)
\\(\bigcirc 3\\)
\\(\bigcirc 5\\)
\\(\bigcirc 25\\)

question 32 (3 points)
solve the problem.

the supply function for a certain car is given by \\(p = 35(3^{q})\\) cars, where \\(p\\) dollars is the price per car and \\(q\\) is the quantity of cars, in thousands, supplied at that price. what quantity will be supplied if the price is \\$25,515 per car?
\\(\bigcirc 8\\) thousand cars
\\(\bigcirc 7\\) thousand cars
\\(\bigcirc 5\\) thousand cars
\\(\bigcirc 6\\) thousand cars

Explanation:

Question 31

Step1: Recall logarithm definition

Let \( \log_{5}(125) = x \). By definition of logarithm, \( 5^x = 125 \).

Step2: Express 125 as power of 5

We know that \( 125 = 5^3 \). So, \( 5^x = 5^3 \).

Step3: Equate exponents

Since the bases are equal, the exponents must be equal. Thus, \( x = 3 \).

Step1: Substitute p value

Given \( p = 35(3^q) \) and \( p = 25515 \). Substitute \( p \): \( 25515 = 35(3^q) \).

Step2: Solve for \( 3^q \)

Divide both sides by 35: \( \frac{25515}{35} = 3^q \). Calculate \( \frac{25515}{35}=729 \). So, \( 3^q = 729 \).

Step3: Express 729 as power of 3

We know \( 729 = 3^6 \). Thus, \( 3^q = 3^6 \).

Step4: Equate exponents

So, \( q = 6 \). Since \( q \) is in thousands, the quantity is 6 thousand cars.

Answer:

3 (the option with "3")

Question 32