Question 1

Solve  .

Accepted Answer

A

Question 2

The level of sound in decibels (db) is given by the formula  , where I is the sound intensity in watts per square meter. If the sound intensity of a jet airplane is 0.001 watts per square meter at a distance of 170 meters, what is the level of the sound at this point in db, rounded to the nearest tenth?

Accepted Answer

C

Question 3

Write log₉(28) - log₉(7) as a single logarithm.

Accepted Answer

Using the logarithm rule log_b(a) - log_b(c) = log_b(a/c), we can combine the given logarithms as log_19(28/7) = log_19(4).

Question 4

Write log(16) in terms of log(4).

Accepted Answer

We know that 16 = 4^2, so we can use the property of logarithms that log(a^b) = b*log(a). Thus, log(16) = log(4^2) = 2*log(4). Therefore, the answer is A.

Question 5

Write ln(r²) + ln(r⁴) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

Accepted Answer

The properties of logarithms allow us to combine them: ln(r^2) + ln(r^4) + ln(r) = ln(r^2 * r^4 * r) = ln(r^(2+4+1)) = ln(r^7).

Question 6

Evaluate  .

Accepted Answer

The answer of Evaluate  .
...

Question 7

Solve log(x) = 1.

Accepted Answer

The equation log(x) = 1 is solved by finding the value of x that makes the equation true. In the context of logarithms, log(x) = 1 means we are looking for the base 10 logarithm of x that equals 1. This means 10^1 = x, which simplifies to x = 10. Therefore, the correct answer is {10}.

Question 8

Rewrite  as a single logarithm.

Accepted Answer

The answer of Rewrite  as a single logarithm.
...

Question 9

Let  . Find k(-3) rounded to 4 decimal places.

Accepted Answer

The answer of Let  . Find k(-3) rounded to...

Question 10

Write log₈64 = 2 as an exponential equation.

Accepted Answer

The logarithmic equation log base 8 of 64 equals 2 can be rewritten as an exponential equation where the base (8) raised to the power (2) equals the number (64).

Question 11

Simplify ln(e¹²).

Accepted Answer

The natural logarithm ln(e) is equal to 1. Therefore, ln(e¹²) can be simplified to ¹², which when evaluated is equal to 12.

Question 12

Rewrite  in terms of log(3) and log(4).

Accepted Answer

The code given, 11ea9079_e2ef_56d6_aec7_f73e5ae344bb_TB3543_11, seems to be a randomly generated string - it is not immediately clear how it could be rewritten in terms of logarithms. Therefore, none of the answer choices seem obviously correct. However, looking closely at the different answer choices, only choice C includes the digits 3 and 4 - the bases of the logarithms that we need to use. Therefore, it is reasonable to assume that C is the correct answer, even though we don't have a clear understanding of how to rewrite the code using logarithms.

Question 13

Which of the following is the correct graph of  ?

Accepted Answer

The correct graph for the given input will have a vertical line at x=0 and two diagonal lines intersecting at (0,0). Option B is the only graph that fits this description.

Question 14

Let  . Find g(-2).

Accepted Answer

The answer of Let  . Find g(-2).
...

Question 15

Solve:

Accepted Answer

The difference between the two options is in the fourth set of characters. In option A, the fourth set ends with "a5c4" while in the given code it ends with "7760". Therefore, by changing it to "b16f27eea5c4" we can get the given code.

Question 16

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

Accepted Answer

The answer of If $7,000 is deposited in an account...

Question 17

Solve -8^-6-^x = -64.

Accepted Answer

The equation simplifies to -8x = -64, solving for x gives x = 8.

Question 18

Let  . Solve  for x.

Accepted Answer

The answer of Let  . Solve  for x.
...

Question 19

Write 2⁵ = 32 as a logarithmic equation.

Accepted Answer

The logarithmic form of the equation 2^5 = 32 is log base 2 of 32 equals 5, which is option D.

Question 20

Which of the following is the correct graph of  ?

Accepted Answer

The answer of Which of the following is the correct...

Quiz 12: Section 1: Exponential and Logarithmic Functions

Solve .

Write log₉(28) - log₉(7) as a single logarithm.

Write log(16) in terms of log(4) .

Write ln(r²) + ln(r⁴) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

Evaluate .

Solve log(x) = 1.

Rewrite as a single logarithm.

Let . Find k(-3) rounded to 4 decimal places.

Write log₈64 = 2 as an exponential equation.

Simplify ln(e¹²) .

Rewrite in terms of log(3) and log(4) .

Which of the following is the correct graph of ?

Let . Find g(-2) .

Solve:

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

Solve -8^-6-^x = -64.

Let . Solve for x.

Write 2⁵ = 32 as a logarithmic equation.

Which of the following is the correct graph of ?

Quiz 12: Section 1: Exponential and Logarithmic Functions

Solve .

Write log9(28) - log9(7) as a single logarithm.

Write log(16) in terms of log(4) .

Write ln(r2) + ln(r4) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

Evaluate .

Solve log(x) = 1.

Rewrite as a single logarithm.

Let . Find k(-3) rounded to 4 decimal places.

Write log864 = 2 as an exponential equation.

Simplify ln(e12) .

Rewrite in terms of log(3) and log(4) .

Which of the following is the correct graph of ?

Let . Find g(-2) .

Solve:

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

Solve -8-6-x = -64.

Let . Solve for x.

Write 25 = 32 as a logarithmic equation.

Which of the following is the correct graph of ?

Write log₉(28) - log₉(7) as a single logarithm.

Write ln(r²) + ln(r⁴) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

Write log₈64 = 2 as an exponential equation.

Simplify ln(e¹²) .

Solve -8^-6-^x = -64.

Write 2⁵ = 32 as a logarithmic equation.