1/1/2018 PRACTICE TEST 4.2
MATH111 K001 Fall 17 Assessments PRACTICE TEST 1.1 Results
PRACTICE TEST 4.2 - Grade Report
Score: 92% (12 of 13 pts)
Submitted: Dec 22 at 4:18am
Question: 1 Grade: 1..0
Express the domain of f (x) = ln (6x − 12) in interval notation.
Your response
(2, ∞)
Solution
The ln (6x − 12) is defined only when 6x − 12x is greater than 0. So, solve the inequality 6x − 12 > 0 to find the domain of the function.
6x − 12 > 0
6x > 12
x > 2
So, the function's domain is (2, ∞) .
Question: 2 Grade: 1..0
I
The Richter scale magnitude, R , of an earthquake of intensity I is defined as R = log ( ), where I0 is a small threshold intensity. Find the
I
0
magnitude of an earthquake with intensity 55,000,000I0 .
If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.
magnitude = 7.74 (100%)
Solution
Substitute 55,000,000I0 into the formula for R and simplify.
55,000,000I
I 0
R = log ( ) = log ( ) = log 55,000,000 = 7.74
I I
0 0
This study source was downloaded by 100000861562950 from CourseHero.com on 02-16-2023 12:16:38 GMT -06:00
https://courses.thinkwell.com/courses/2593/exercises/1079637/results/1213333 1/7
https://www.coursehero.com/file/31039062/PRACTICE-TEST-42pdf/
, 1/1/2018 PRACTICE TEST 4.2
Question: 3 Grade: 1..0
Use a calculator to evaluate (log 15)×(ln 19).
If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.
(log 15)×(ln 19) = 3.46 (100%)
Solution
Keystrokes: LOG 15 × LN 19 ENTER
( log 15) × ( ln 19) = 3.462929 ≈ 3.46
Question: 4 Grade: 1..0
Evaluate ln 1 + 2e
ln 3
without using a calculator.
ln 1 + 2e
ln 3
= 6 (100%)
Solution
Use the properties that ln 1 = 0 , ln e = 1 , and eln x
= x to simplify.
ln 3
ln 1 + 2e
0+2 ⋅ 3
6
Question: 5 Grade: 1..0
3
Evaluate ln e 5 without using a calculator.
If the answer is not an integer, enter it as a fraction.
3
ln e 5 = 3/5 (100%)
Solution
3
Since ln e
x
= x, ln e 5 =
3
.
5
This study source was downloaded by 100000861562950 from CourseHero.com on 02-16-2023 12:16:38 GMT -06:00
https://courses.thinkwell.com/courses/2593/exercises/1079637/results/1213333 2/7
https://www.coursehero.com/file/31039062/PRACTICE-TEST-42pdf/
MATH111 K001 Fall 17 Assessments PRACTICE TEST 1.1 Results
PRACTICE TEST 4.2 - Grade Report
Score: 92% (12 of 13 pts)
Submitted: Dec 22 at 4:18am
Question: 1 Grade: 1..0
Express the domain of f (x) = ln (6x − 12) in interval notation.
Your response
(2, ∞)
Solution
The ln (6x − 12) is defined only when 6x − 12x is greater than 0. So, solve the inequality 6x − 12 > 0 to find the domain of the function.
6x − 12 > 0
6x > 12
x > 2
So, the function's domain is (2, ∞) .
Question: 2 Grade: 1..0
I
The Richter scale magnitude, R , of an earthquake of intensity I is defined as R = log ( ), where I0 is a small threshold intensity. Find the
I
0
magnitude of an earthquake with intensity 55,000,000I0 .
If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.
magnitude = 7.74 (100%)
Solution
Substitute 55,000,000I0 into the formula for R and simplify.
55,000,000I
I 0
R = log ( ) = log ( ) = log 55,000,000 = 7.74
I I
0 0
This study source was downloaded by 100000861562950 from CourseHero.com on 02-16-2023 12:16:38 GMT -06:00
https://courses.thinkwell.com/courses/2593/exercises/1079637/results/1213333 1/7
https://www.coursehero.com/file/31039062/PRACTICE-TEST-42pdf/
, 1/1/2018 PRACTICE TEST 4.2
Question: 3 Grade: 1..0
Use a calculator to evaluate (log 15)×(ln 19).
If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.
(log 15)×(ln 19) = 3.46 (100%)
Solution
Keystrokes: LOG 15 × LN 19 ENTER
( log 15) × ( ln 19) = 3.462929 ≈ 3.46
Question: 4 Grade: 1..0
Evaluate ln 1 + 2e
ln 3
without using a calculator.
ln 1 + 2e
ln 3
= 6 (100%)
Solution
Use the properties that ln 1 = 0 , ln e = 1 , and eln x
= x to simplify.
ln 3
ln 1 + 2e
0+2 ⋅ 3
6
Question: 5 Grade: 1..0
3
Evaluate ln e 5 without using a calculator.
If the answer is not an integer, enter it as a fraction.
3
ln e 5 = 3/5 (100%)
Solution
3
Since ln e
x
= x, ln e 5 =
3
.
5
This study source was downloaded by 100000861562950 from CourseHero.com on 02-16-2023 12:16:38 GMT -06:00
https://courses.thinkwell.com/courses/2593/exercises/1079637/results/1213333 2/7
https://www.coursehero.com/file/31039062/PRACTICE-TEST-42pdf/
