Question 1

The earthquake that occurred in Chile in 1960 was 1000 times more intense than the one that occurred in Wyoming in 1959, which had a Richter magnitude of 6.5. Determine Chile's earthquake magnitude.
A) 7.5
B) 8.5
C) 9.5
D) 8.0

Accepted Answer

The magnitude increase on the Richter scale is logarithmic, meaning each whole number increase represents a tenfold increase in measured amplitude. To be 1000 times more intense, the earthquake would need to be 3 magnitudes higher (10^3 = 1000), making the Chile earthquake's magnitude 6.5 + 3 = 9.5.

Question 2

Two earthquakes were registered the same day in a small south Pacific island, the first one with Richter magnitude 4.4 and the second one with Richter magnitude 3.9. Approximately how many times more intense was the first earthquake than the second one? Round your answer to the nearest tenth.

Accepted Answer

The answer of Two earthquakes were registered the same day...

Question 3

The most intense recorded earthquake in the southeast states during a period of time had Richter magnitude 3.1. If an earthquake were to strike one of these states next year that was four times as intense as the current record, what would its Richter magnitude be?
A) 3.7
B) 3.6
C) 3.4
D) 7.1

Accepted Answer

The Richter scale is logarithmic, meaning each whole number increase represents a tenfold increase in measured amplitude. An earthquake that is four times as intense would be represented by an increase of 0.6 on the Richter scale (since $10^{0.6} \approx 4$). Therefore, adding 0.6 to the current record of 3.1 gives a magnitude of 3.7.

Question 4

Evaluate log₂(8xy) assuming that log₂x = 12.7 and log₂y = 7.1.

Accepted Answer

The answer of Evaluate log₂(8xy) assuming that log₂x = 12.7...

Question 5

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Accepted Answer

The answer of Evaluate assuming that log₃x =...

Question 6

Evaluate assuming that log₇x = 11.3 and log₇y = 4.5.

Accepted Answer

The answer of Evaluate assuming that log₇x = 11.3...

Question 7

Evaluate assuming that log₇x = 3.7 and log₇y = 4.1.

Accepted Answer

The answer of Evaluate assuming that log₇x =...

Question 8

Evaluate log₅(x³y²) assuming that log₅x = 11.1 and log₅y = 6.1.

Accepted Answer

The answer of Evaluate log₅(x³y²) assuming that log₅x = 11.1...

Question 9

Evaluate log₃(x⁴y⁶) assuming that log₃x = 9.1 and log₃y = 4.5.

Accepted Answer

The answer of Evaluate log₃(x⁴y⁶) assuming that log₃x =...

Question 10

Suppose N is a positive integer such that log N $\approx$ 51.2. How many digits does N have?
A) 51
B) 52
C) 3
D) Cannot be determined

Accepted Answer

The number of digits in a number N can be found using the formula for the number of digits in base 10, which is $\lceil \log_{10} N \rceil$. Given $\log N \approx 51.2$, this implies $\log_{10} N \approx 51.2$. Therefore, N has approximately 52 digits, since the number of digits is the integer part of the logarithm plus one.

Question 11

Suppose m and n are positive integers such that log m $\approx$ 143.33 and log n $\approx$ 217.34. How many digits does mn have?
A) 361
B) 31,151
C) 360
D) Cannot be determined

Accepted Answer

The number of digits of a number x is given by the formula floor(log10(x)) + 1. Since log(mn) = log(m) + log(n), we have log(mn) ≈ 143.33 + 217.34 = 360.67. Therefore, the number of digits in mn is floor(360.67) + 1 = 361.

Question 12

Suppose x is such that   . Evaluate  
 .
A) 115.99
B) 24.01
C) 1.522
D) 3,219.30

Accepted Answer

The answer of Suppose x is such that  ...

Question 13

Suppose x is such that   . Evaluate   . Round your answer to three decimal places.
A) 245.25
B) 187.250
C) 7.457
D) 6,271.25

Accepted Answer

The answer of Suppose x is such that  ...

Question 14

Evaluate   assuming that  
 .

Accepted Answer

The answer of Evaluate   assuming that  
...

Question 15

Evaluate Assuming that   .
A) 1,050
B) 525
C) 60.5
D) 105.25

Accepted Answer

The answer of Evaluate Assuming that   .
A) 1,050
B)...

Question 16

Evaluate Assuming that   .
A) -16.1
B) 16.1
C) -17.9
D) 17.9

Accepted Answer

The answer of Evaluate Assuming that   .
A) -16.1
B)...

Question 17

Find all numbers x that satisfy the equation 
   . Round your answer to two decimal places.

Accepted Answer

The answer of Find all numbers x that satisfy the...

Question 18

Find all numbers x that satisfy the equation 
 
 . Round your answer to two decimal places.

Accepted Answer

The answer of Find all numbers x that satisfy the...

Question 19

Find all numbers x that satisfy the equation   .
A) 7
B) 4
C) 28
D) 0.57

Accepted Answer

The answer of Find all numbers x that satisfy the...

Question 20

Find the number of digits in the given number.  
A)  has 935 digits
B)  has 3,102 digits
C)  has 934 digits
D)  has 933 digits

Accepted Answer

The answer of Find the number of digits in the...

Quiz 4: Exponential Functions, Logarithms, and E

The earthquake that occurred in Chile in 1960 was 1000 times more intense than the one that occurred in Wyoming in 1959, which had a Richter magnitude of 6.5. Determine Chile's earthquake magnitude.

Two earthquakes were registered the same day in a small south Pacific island, the first one with Richter magnitude 4.4 and the second one with Richter magnitude 3.9. Approximately how many times more intense was the first earthquake than the second one? Round your answer to the nearest tenth.

The most intense recorded earthquake in the southeast states during a period of time had Richter magnitude 3.1. If an earthquake were to strike one of these states next year that was four times as intense as the current record, what would its Richter magnitude be?

Evaluate log2(8xy) assuming that log2x = 12.7 and log2y = 7.1.

Evaluate assuming that log3x = 12.3 and log3y = 7.9.

Evaluate assuming that log7x = 11.3 and log7y = 4.5.

Evaluate assuming that log7x = 3.7 and log7y = 4.1.

Evaluate log5(x3y2) assuming that log5x = 11.1 and log5y = 6.1.

Evaluate log3(x4y6) assuming that log3x = 9.1 and log3y = 4.5.

Suppose N is a positive integer such that log N ≈\approx≈ 51.2. How many digits does N have?

Suppose m and n are positive integers such that log m ≈\approx≈ 143.33 and log n ≈\approx≈ 217.34. How many digits does mn have?

Suppose x is such that . Evaluate .

Suppose x is such that . Evaluate . Round your answer to three decimal places.

Evaluate assuming that .

Evaluate Assuming that .

Evaluate Assuming that .

Find all numbers x that satisfy the equation . Round your answer to two decimal places.

Find all numbers x that satisfy the equation . Round your answer to two decimal places.

Find all numbers x that satisfy the equation .

Find the number of digits in the given number.

Evaluate log₂(8xy) assuming that log₂x = 12.7 and log₂y = 7.1.

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Evaluate assuming that log₇x = 11.3 and log₇y = 4.5.

Evaluate assuming that log₇x = 3.7 and log₇y = 4.1.

Evaluate log₅(x³y²) assuming that log₅x = 11.1 and log₅y = 6.1.

Evaluate log₃(x⁴y⁶) assuming that log₃x = 9.1 and log₃y = 4.5.

Suppose N is a positive integer such that log N $\approx$ 51.2. How many digits does N have?

Suppose m and n are positive integers such that log m $\approx$ 143.33 and log n $\approx$ 217.34. How many digits does mn have?