2.9 · Logarithmic Expressions

Try each one on paper first, then tap to check.

1. 1.

   Rewrite as an exponent: $\log_2 64 = 6$
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2. 2.

   Rewrite as an exponent: $\log_4 \tfrac{1}{64} = -3$
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3. 3.

   Rewrite as an exponent: $\log_{25} 125 = \tfrac32$
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4. 4.

   Rewrite as a log: $10^3 = 1000$
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5. 5.

   Rewrite as a log: $16^{5/2} = 1024$
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6. 6.

   Rewrite as a log: $10^{-2} = \tfrac{1}{100}$
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7. 7.

   No calculator: $\log_5 625$
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8. 8.

   No calculator: $\log 100{,}000$
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9. 9.

   No calculator: $\log_{27} 81$
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10. 10.

    Calculator, 3 decimals: $\log 140$
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11. 11.

    Calculator, 3 decimals: $\log_9 120$
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12. 12.

    Calculator, 3 decimals: $\log_3 18$
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13. 12 (log scale).

    Plot on a base 10 logarithmic scale (label axis, show math): Midichlorians found in cells.

    Person	Midichlorians
    Chewbacca	1
    Han Solo	330
    Luke Skywalker	125,000
    Yoda	2,750,000
    Anakin Skywalker	20,000

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14. 13.

    Plot on a base 2 logarithmic scale: errors per section.

    Person	Errors per section
    Bean	5
    Brust	68
    Sullivan	24
    Kelly	15
    New Teacher	300

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15. 14.

    Richter scale (base 10). Earthquake A = 3.5, B = 6.0, C = 8.5.
    Which statement most accurately describes how much more intense C was than A?
    (A) 5 times · (B) 50 times · (C) $10^5$ times · (D) $\log 5$ times
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16. 15.

    Same scale (A = 3.5, B = 6.0, C = 8.5). Which is true?
    (A) The increase A→B is greater than B→C.
    (B) The increase A→B is less than B→C.
    (C) B is as many times more intense than A as C is than B.
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