Lesson test: Logarithms

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Logarithms

1.[2p]
What does $\log_{b} y = x$ assert?

That $b^{x} = y$

Correct

That $y^{x} = b$

The answer is: That $b^x = y$

That $x^{b} = y$

The answer is: That $b^x = y$

That $b \times x = y$

The answer is: That $b^x = y$

2.[1p]
Evaluate $\log_{2} 32$ .

CorrectNot quite: 5

3.[3p]
Solve $3^{x} = 200$ , to three decimal places.

CorrectNot quite: 4.823

4.[2p]
Why is there no logarithm of a negative number?

No power of a positive base is ever negative, so nothing maps there

Correct

Because logarithms are always positive

The answer is: No power of a positive base is ever negative, so nothing maps there

Because the third law would fail

The answer is: No power of a positive base is ever negative, so nothing maps there

Because negative numbers have no square roots

The answer is: No power of a positive base is ever negative, so nothing maps there

5.[3p]
Which of these are true laws of logarithms?

Select all that apply

$\log (M N) = \log M + \log N$

Correct

$\log (M^{k}) = k \log M$

Correct

$\log (M / N) = \log M - \log N$

Correct

$\log (M + N) = \log M \times \log N$

The answer is: $\log(MN) = \log M + \log N$, $\log(M^k) = k \log M$, $\log(M/N) = \log M - \log N$

6.[3p]
Money grows at 5 per cent a year. How many years does it take to double?

CorrectNot quite: 14.21

7.[3p]
Carbon-14 has a half-life of 5730 years. A sample retains 22 per cent of its original carbon-14. What is its age in years?

CorrectNot quite: 12517

8.[2p]
A solution has a hydrogen ion concentration of $3.2 \times 10^{- 4}$ mol per litre. What is its pH?

CorrectNot quite: 3.50

9.[2p]
An increase of 30 decibels corresponds to a thousandfold increase in sound intensity.

True

Correct

False

The answer is: True

1.[2p] What does logby=x assert?

2.[1p] Evaluate log232.

3.[3p] Solve 3x=200, to three decimal places.

4.[2p] Why is there no logarithm of a negative number?

5.[3p] Which of these are true laws of logarithms?

6.[3p] Money grows at 5 per cent a year. How many years does it take to double?

7.[3p] Carbon-14 has a half-life of 5730 years. A sample retains 22 per cent of its original carbon-14. What is its age in years?

8.[2p] A solution has a hydrogen ion concentration of 3.2×10-4 mol per litre. What is its pH?

9.[2p] An increase of 30 decibels corresponds to a thousandfold increase in sound intensity.

1.[2p]
What does $\log_{b} y = x$ assert?

2.[1p]
Evaluate $\log_{2} 32$ .

3.[3p]
Solve $3^{x} = 200$ , to three decimal places.

4.[2p]
Why is there no logarithm of a negative number?

5.[3p]
Which of these are true laws of logarithms?

6.[3p]
Money grows at 5 per cent a year. How many years does it take to double?

7.[3p]
Carbon-14 has a half-life of 5730 years. A sample retains 22 per cent of its original carbon-14. What is its age in years?

8.[2p]
A solution has a hydrogen ion concentration of $3.2 \times 10^{- 4}$ mol per litre. What is its pH?

9.[2p]
An increase of 30 decibels corresponds to a thousandfold increase in sound intensity.