Logarithms II - Challenging

Question 1: Find

x

:

2 = \log_{8} x

A

256

B

64

C

16

D

49

Question 2: Find

x

:

x = \log_{3} 243

A

9

B

81

C

27

D

5

Question 3: Solve

\log_{2} 8 + \log_{8} 2

A

3 \frac{1}{3}

B

1

C

16

D

4

Question 4: Express

\log_{7} x

as multiple of

\log_{10} x

A

\log_{10} x - \log_{3} x

B

\log_{10} x \log_{7} 10

C

\log_{10} x \log_{3} x

D

\frac{\log_{10} x}{\log_{3} x}

Question 5: Express

\log_{4} 17

in terms of the logarithms base

10

A

\log_{10} 4 / \log_{10} 17

B

4 \log_{10} 17

C

\log_{10} 17 / \log_{10} 4

D

17 \log_{10} 4

Question 6: Simplify

3 \log_{a} 2 x + 2 \log_{a} x^{2} - 6 \log_{a} x

A

\log_{a} 8 x

B

\log_{a} 6 x^{2}

C

2 \log_{a} x

D

- \log_{a} (x - x^{2})

Question 7: Simplify

2 \log_{a} \frac{1}{2} x - \log_{a} 3 x + 2 \log_{a} 2 x

A

3 \log_{a} x

B

\log_{a} \frac{3}{4} x^{3}

C

\log_{a} (\frac{x^{3}}{3})

D

\log_{a} \frac{4}{3} x^{2}

Question 8: Find

x

:

6 \log_{a} x \frac{1}{3} - \log_{a} 2 x = 2 \log_{a} x

A

x = 1

B

x = 2

C

x = \frac{1}{2}

D

x = \sqrt{2}

Question 9: Find

x

:

12^{\log_{12} 5} = x

A

x = 4

B

x = \frac{1}{5}

C

x = 12

D

x = 5

Question 10: Find

y

in terms of

x

:

2 \log_{a} x + 3 \log_{a} y = 3 \log_{a} 2 x + 3 \log_{a} \sqrt{y}

A

y = \frac{1}{2} x^{4}

B

y = 3 \sqrt{x^{5}}

C

y = \frac{1}{4} x^{3}

D

y = 4 \sqrt[3]{x^{2}}

Test: Logarithms II - Challenging

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