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Algebra II / Mr. Hansen |
Name:
_________________________ |
Test through §6-11
Time limit: 26 minutes (39 minutes for extended
time). Calculator is allowed throughout. Point values are shown on the
board.
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Part I: Proof (25 points) |
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1. |
State and prove the Change
of Base formula for logarithms. Use letters a and b for the two bases involved, and use x for the unknown value whose logarithm is being computed. Be
sure to include all the assumptions regarding a, b, and x. |
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Part II: Short Answer (5 points each, little or no
partial credit) |
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All calculator results must
be correct to at least 3 decimal places. |
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2. |
Whenever we give a
calculator-based answer on a quiz or test, we must provide at least ____ decimal
places of accuracy. (This is supposed to be a “gift” question.) |
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3. |
Compute log7 45:
_______________ |
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I am thinking of a number, x. I will not tell you what x is, but I will tell you that logx
2 » .25, logx
3 » .4, and logx
5 » .6. Estimate each of
the following. |
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4. |
logx 15 » ____________________ |
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5. |
logx 510
» ____________________ |
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6. |
logx (5/3) » ____________________ |
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7. |
Estimate the value of x itself: ___________________ |
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8. |
Give a short reason for
your answer to #7: ____________________ |
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9. |
Find an approximation for y if 10y = 347. ____________________ |
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10. |
Write 300300 in
scientific notation: ____________________ |
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11. |
Estimate |
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12. |
Write an exponential
function where y is equal to something:
_____________________ |
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13. |
Rewrite your equation in
#12 in logarithmic form: ____________________________ |
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14. |
What name in mathematics do
we give to an “adjustable constant”? Hint:
The word starts with the letter P. _____________________________ |
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15. |
Simplify the expression
that is written on the board. |
