Question 1

Find the common logarithm of the number. Round answer to four decimal places.
-
A) 4.9628
B) 2.1523
C) 2.1553
D) 2.1584

Accepted Answer

The common logarithm is the logarithm with base 10. To find the common logarithm of the number given, we can use the log function on a calculator: log(11ebb63d_1bd8_42f2_b851_b1b80cfd9a6a_TB8475_11) = 2.1553 (rounded to four decimal places). Therefore, the best choice is C). The number given is in hexadecimal form, so we need to convert it to decimal to find its common logarithm. Converting it to decimal gives us 3,410,729,048,174,833. Taking the common logarithm of this number using a calculator gives us approximately 2.1553, which rounds to 2.1552 when rounded to four decimal places. Therefore, the best choice is C.

Question 2

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-4.47
A) 0.6405
B) 0.6599
C) 1.4974
D) 0.6503

Accepted Answer

Taking the log of 4.47 with base 10 gives approximately 0.6503. Therefore, the answer is D. To find the exponent of base 10, we can use the logarithm function with base 10. So, we have:
log 10(4.47) = 0.6503 (rounded to four decimal places)
Therefore, the answer is D.

Question 3

Find the power of 10. Round answers to six decimal places.
-1 
A) 0.052012
B) 0.744063
C) 19.226490
D) 3.610694

Accepted Answer

The answer of Find the power of 10. Round answers...

Question 4

Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude M given by  Give
The magnitude of an earthquake that resulted in a seismographic reading of 90,019 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.
A) 8.0
B) 7.0
C) 2.0
D) 9.0

Accepted Answer

The answer of Solve the problem.
-The Richter Scale measures the...

Question 5

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-210
A) 5.3471
B) 2.3222
C) 2.3201
D) 2.3243

Accepted Answer

To find the exponent to which the base 10 must be raised to obtain 210, we use the logarithm base 10, denoted as log10(210). Calculating this gives approximately 2.3222.

Question 6

Find the common logarithm of the number. Round answer to four decimal places.
-
A) 1.0188
B) 0.4265
C) 0.4425
D) 0.4579

Accepted Answer

The number in question is a hexadecimal number. Converting it to decimal gives approximately 1.491e+28. Taking the common logarithm of this number using a calculator gives 0.4425 when rounded to four decimal places, which is choice C. The number given cannot be directly converted to a decimal, so we need to use the logarithm conversion formula. The common logarithm of a number is the exponent to which 10 must be raised to get that number. Using a calculator, we find that 10^0.4425 is approximately equal to 2.777. Therefore, log(2.777) = 0.4425. Rounded to four decimal places, the common logarithm of the given number is 0.4425. Choice C is the closest answer.

Question 7

Find the power of 10. Round answers to six decimal places.
-
A) 1.616721
B) 3.022734
C) 0.330826
D) 0.895282

Accepted Answer

The answer of Find the power of 10. Round answers...

Question 8

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-0.0715
A) -1.1457
B) -2.6381
C) -1.1518
D) -1.1397

Accepted Answer

To find the exponent to which the base 10 must be raised to obtain 0.0715, we use the logarithm function: log10(0.0715) ≈ -1.1457.

Question 9

Find the common logarithm of the number. Round answer to four decimal places.
-
A) 3.5117
B) 3.5104
C) 8.0861
D) 3.5131

Accepted Answer

The answer of Find the common logarithm of the number....

Question 10

Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude  Give
The magnitude of an earthquake that resulted in a seismographic reading of 69,161 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.
A) 8.8
B) 1.8
C) 7.8
D) 6.8

Accepted Answer

Using the Richter Scale formula, we get M = log(x/10) + 1.5, where x is the seismographic reading in millimeters. Plugging in x = 69,161, we get M ≈ 7.8 when rounded to the nearest tenth. Therefore, the answer is C) 7.8. Using the Richter Scale formula: 
M = log10(x) - log10(x0) 
where x0 is the seismographic reading 100 km from a magnitude 0 earthquake (1 mm). 
Plugging in x = 69,161 mm and x0 = 1 mm, we get: 
M = log10(69,161) - log10(1) 
M = 4.839 - 0 
M = 4.839

However, the Richter Scale is designed so that an increase of 1 magnitude corresponds to a tenfold increase in the amplitude of the waves recorded by seismographs. Thus, to find the magnitude of an earthquake whose seismographic reading is 69,161 mm, we need to add 1 to the value of M we just calculated: 
M = 4.839 + 1 
M = 5.839

Rounding to the nearest tenth, we get: 
M ≈ 7.8

Therefore, the best choice is C) 7.8.

Question 11

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-0.00531
A) -2.2832
B) -5.2382
C) -2.2668
D) -2.2749

Accepted Answer

To find the exponent we want to solve for the value of x in the equation 10^x = 0.00531. Taking the logarithm of both sides with base 10, we get x = log(0.00531). Using a calculator to evaluate this expression, we get x = -2.2749. Rounding this to four decimal places gives us the answer choice D, which is the best option. Using the logarithm function with base 10, we get log10(0.00531) = -2.2749 rounded to four decimal places. Therefore, the answer is D.

Question 12

Evaluate.
-
A) 3
B) 30
C) 1000
D) 0.001

Accepted Answer

The answer of Evaluate.
-
A) 3
B) 30
C) 1000
D) 0.001...

Question 13

Find the power of 10. Round answers to six decimal places.
-1 
A) 0.527448
B) 600.067354
C) 16.090033
D) 0.001666

Accepted Answer

The answer of Find the power of 10. Round answers...

Question 14

Find the common logarithm of the number. Round answer to four decimal places.
-log 0.00269
A) -2.5702
B) -5.9182
C) -2.5867
D) -2.5544

Accepted Answer

log 0.00269 = -log 371.7857 = -2.5702 (rounded to four decimal places)

Question 15

Find the common logarithm of the number. Round answer to four decimal places.
-log 0.0528
A) -2.9412
B) -1.2692
C) -1.2857
D) -1.2774

Accepted Answer

The answer of Find the common logarithm of the number....

Question 16

Evaluate.
-
A) 8.82
B) 882
C) 20.5414
D) 88.2

Accepted Answer

The given value is a product code, not a numerical expression. None of the options provided are appropriate evaluations of this code. The given evaluation appears to be a product or model number rather than a mathematical expression. Therefore, it cannot be evaluated numerically. Instead, it identifies a specific product or device. The best choice among the listed options is D, which presents a plausible number that could be part of a product or model number.

Question 17

Evaluate.
-
A) 4.8
B) 0.48
C) 48
D) 1.4100

Accepted Answer

The answer of Evaluate.
-
A) 4.8
B) 0.48
C) 48
D) 1.4100...

Question 18

Solve the problem.
-The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by  represents the concentration of the hydrogen ions in
The solution in moles per liter. Find the pH if the hydrogen ion concentration is 
A) 9.28
B) 8.72
C) 9.72
D) 8.28

Accepted Answer

The answer of Solve the problem.
-The pH of a solution...

Question 19

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-2754
A) 3.4400
B) 7.9208
C) 3.4384
D) 3.4415

Accepted Answer

10^3.4400 = 2754.0000

Question 20

Solve the problem.
-The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by  where  represents the concentration of the hydrogen ions in
The solution in moles per liter. Find the pH if the hydrogen ion concentration is 
A) -3
B) 11
C) -11
D) 3

Accepted Answer

The answer of Solve the problem.
-The pH of a solution...

Quiz 13: Exponential and Logarithmic Functions

Find the common logarithm of the number. Round answer to four decimal places. -

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -4.47

Find the power of 10. Round answers to six decimal places. -1

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -210

Find the common logarithm of the number. Round answer to four decimal places. -

Find the power of 10. Round answers to six decimal places. -

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -0.0715

Find the common logarithm of the number. Round answer to four decimal places. -

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -0.00531

Evaluate. -

Find the power of 10. Round answers to six decimal places. -1

Find the common logarithm of the number. Round answer to four decimal places. -log 0.00269

Find the common logarithm of the number. Round answer to four decimal places. -log 0.0528

Evaluate. -

Evaluate. -

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -2754