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MathQuiz 4.2
University of Sydney
School of Mathematics
and Statistics
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Logarithmic Functions - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Is the following statement true or false?

        ln e5 = eln5 = 5.
a) True.   b) False.

 

Your answer is correct.
The natural log and exponential functions are inverse of each other so the statement is true.
Not correct. Choice (b) is false.
The natural log and exponential functions are inverse of each other so the statement is true.
Question 2 lion

Which of the following is the value of   ln- 2   correct to 3 decimal places?
a) -0.693.   b) 0.135.
c) 0.   d) None of the above.

 

Not correct. Choice (a) is false.
Try again, this is   -ln2.
Not correct. Choice (b) is false.
Try again, this is  e-2 .
Not correct. Choice (c) is false.
Try again, you may not have noticed the error message on your calculator.
Your answer is correct.
The natural log function is only defined for numbers greater than 0 so  ln- 2 is not defined.
Question 3 lion

Which of the following is   2ln 3+ 4   correct to 3 decimal places?
a) 6.197.   b) 3.8918.
c) 44.171.   d) 10.197.

 

Your answer is correct.
2 ln3 + 4 = 2 ×1.0986+ 4 = 2.1972+ 4 = 6.1972.
Not correct. Choice (b) is false.
Try again, this is   2 ln(3+ 4).
Not correct. Choice (c) is false.
Try again, this is   2e3 + 4.
Not correct. Choice (d) is false.
Try again, this is   2(ln 3+ 4).
Question 4 lion

Which of the following solves   ln(- 2x+ 4) = 1.099   for x correct to 2 decimal places?
a) x = -0.50.   b) x = 0.03.
c) x = 0.50.   d) None of the above.

 

Not correct. Choice (a) is false.
Try again, this gives ln 5 /= 1.099.
Not correct. Choice (b) is false.
Try again, exponentiate both sides before trying to manipulate the equation.
Your answer is correct.
Exponentiate both sides which gives   1 -2x +4 = 3.00 ==> - 2x = - 1 ==> x = 2 .
Not correct. Choice (d) is false.
Try again, -2x + 4 is not necessarily negative.
Question 5 lion

Which of the following solves   log102x +3 = 7   for x exactly?
a) x = 499993.5 .   b) x = 5000.
c) e4 x = --. 2   d) x = 102.

 

Not correct. Choice (a) is false.
Try again, take away 3 from both sides before raising to the power of 10.
Your answer is correct.
log10 2x+ 3 = 7 ==> log102x = 4
Raise both sides to the power of 10 and
2x = 104 = 10000 ==> x = 5000 .
Not correct. Choice (c) is false.
Try again, you need to raise to the power 10, not  e.
Not correct. Choice (d) is false.
Try again, you have solved 2x +3 = 7 and then raise to the power of 10.