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Logarithmic Functions - Quiz 2   Last unanswered question  Question  Next unanswered question

Question 1 lion

Is the following statement true or false?
    ln e-5   is undefined.
a) True.   b) False.

 

Not correct. Choice (a) is false.
The natural log and exponential functions are inverse of each other so the statement is false  lne-5 = - 5.
Your answer is correct.
The natural log and exponential functions are inverse of each other so the statement is false  ln e-5 = - 5.
Question 2 lion

Which of the following is the value of   ln2   correct to 3 decimal places?
a) -0.693.   b) 7.389.
c) 0.693.   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  e2.
Your answer is correct.
Not correct. Choice (d) is false.
The domain of the natural log function is only numbers greater than 0 so  ln 2 is defined.
Question 3 lion

Which of the following is   3ln2 + 5   correct to 3 decimal places?
a) 5.838.   b) 7.079.
c) 27.167.   d) 17.079.

 

Not correct. Choice (a) is false.
Try again, this is   3ln(2 + 5).
Your answer is correct.
3 ln2 + 5 = 3 × 0.6931+ 5 = 2.0794+ 5 = 7.0794.
Not correct. Choice (c) is false.
Try again, this is   3e2 + 5.
Not correct. Choice (d) is false.
Try again, this is   3(ln2+ 5).
Question 4 lion

Which of the following solves   ln(2x- 3) = 1.386   for x correct to 2 decimal places?
a) x = 3.50 .   b) x = 0.50 .
c) x = 8.96 .   d) None of the above.

 

Your answer is correct.
Exponentiate both sides which gives  2x - 3 = 4.00 ⇒ 2x = 7 ⇒ x = 3.50.
Not correct. Choice (b) is false.
Try again, this makes the argument of  ln   negative which is not defined.
Not correct. Choice (c) is false.
Try again, exponentiate both sides before trying to manipulate the equation.
Not correct. Choice (d) is false.
Try again, 2x - 3 is not necessarily negative.
Question 5 lion

Which of the following solves   log104x+ 5 = 6   for x exactly?
a) x = 249998.75 .   b) e x = 4 .
c) x = 5000.   d) x = 100.25.

 

Not correct. Choice (a) is false.
Try again, take away 5 from both sides before raising to the power of 10.
Not correct. Choice (b) is false.
Try again, you need to raise to the power 10, not  e .
Your answer is correct.
log10 4x+ 5 = 6 ⇒ log104x = 1
Raise both sides to the power of 10 and
4x = 101 = 10 ⇒ x = 2.50.
Not correct. Choice (d) is false.
Try again, you have solved 4x+ 5 = 6 and then raised to the power of 10.