Logarithmic Functions - Quiz 3


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Logarithmic Functions - Quiz 3 Question

Question 1

Is the following statement true or false?
$ln e-2 = eln-2.$

Not correct. Choice (a) is false.

The natural log and exponential functions are inverse of each other but one needs to be careful with negative numbers since $ln- 2$ is undeﬁned.

Your answer is correct.

The natural log and exponential functions are inverse of each other but one needs to be careful with negative numbers. The statement is false since $lne-2 = ln(e2)- 1 = - ln e2 = - eln2.$

Question 2

Which of the following is the value of $ln- 3$ correct to 3 decimal places?

Not correct. Choice (a) is false.

Try again, this is $- ln3.$

Not correct. Choice (b) is false.

Try again, this is $e-3 .$

Not correct. Choice (c) is false.

Try again, this is $- e3.$

Your answer is correct.

The domain of the natural log function is only numbers greater than 0 so $ln- 3$ is deﬁned.

Question 3

Which of the following is $4 - 2 ln 3$ correct to 3 decimal places?

Not correct. Choice (a) is false.

Try again, this is $4+ 2ln3 .$

Not correct. Choice (b) is false.

Try again, you have not rounded correctly

Your answer is correct.

$4 - 2ln 3 = 4 - 2 × 1.0986 = 4- 2.1972 = 1.0828.$

Not correct. Choice (d) is false.

Try again, this is $4 = 2ln3$ rounded incorrectly.

Question 4

Which of the following solves $4- ln 3x = 1.386$ for $x$ correct to 2 decimal places?

Not correct. Choice (a) is false.

Try again, you have solved $ln3x - 4 = 1.386 .$

Your answer is correct.

Get $ln3x$ by itself and then exponentiate
$ln3x = 4- 1.386 ⇒ ln3x = 2.614 ⇒ 3x = 13.654 ⇒ x = 4.551.$

Not correct. Choice (c) is false.

Try again, isolate $ln 3x$ before exponentiating both sides of the equation.

Not correct. Choice (d) is false.

Try again, isolate $ln 3x$ before exponentiating both sides of the equation.

Question 5

Which of the following solves $log10(2x+ 3) = 2$ for $x$ exactly?

Not correct. Choice (a) is false.

Try again, you have taken away 3 from both sides before raising to the power of 10.

Not correct. Choice (b) is false.

Try again, you have solved $2x + 3 = 2$ and then raised to the power of 10.

Not correct. Choice (c) is false.

Try again, you need to raise to the power 10, not $e.$

Your answer is correct.

$log10(2x + 3) = 2$
Raise both sides to the power of 10 and
$2x + 3 = 102 = 100 ⇒ 2x = 97 ⇒ x = 48.5.$