Buzz: Questions & Answers

I'm not sure what trouble you were having.I had to reformat the text to account for the HTML but, I didn't make any substantive changes. It worked in my test.

Type: MC
1) Which of the following is equivalent to `y=log_7 x`?
@[Always] Remember, a logarithm “gives” as the y-value the exponent we must raise the base, 7, to in order to get x.
a. `y=x^7`
b. `x=y^7`
*c. `x=7^y`
d. `y=x^(1/7)`

Type: MC
2) If the graph of `y=6^x` is reflected across the line `y=x` then the resulting curve has an equation of
@[Always] This question is testing to see if you know that reflecting across the line y=x always produces the inverse, which in this case is `y=log_6 x`.
a. `y=-6^x`
*b. `y=log_6 x`
c. `x=log_6 y`
d. `x=y^6`

Type: MC
3) The value of `log_5 167` is closest to which of the following?
@[Always] `5^3.18=167.003...~~167`
a. `2.67`
b. `1.98`
c. `4.58`
*d. `3.18`

Type: MC
4) Which of the following represents the `y`-intercept of the function `y=log(x+1000)-8`?
@[Always] `y=log(0+1000)-8 = log(1000)-8` `=log_10(1000)-8=3-8=-5`
a. `-8`
*b. `-5`
c. `3`
d. `5`

Type: P
Id: dd33e7e322c34d96b87f6861f58655ab
5) Determine the value for each of the following logarithms. (Easy)

Type: F
6) `log_2(32)=`_____
a. 5

Type: F
7) `log_7(49)=`_____
a. 5

Type: F
8) `log_3(6561)=`_____
a. 8

Type: F
9) `log_4(1024)=`_____
a. 5

Type: P
Id: 847dd9d28699481eab42c61c8f0ff62c
10) Determine the value for each of the following logarithms. (Medium)

Type: F
11) `log_2(1/64)=`_____
@[Always] `log_2(1/64)=-6` Because `2^-6=1/2^6=1/64`
a. -6

Type: F
12) `log_3(1)=`_____
@[Always] `log_3(1)=0` Because `3^0=1`
a. 0

Type: F
13) `log_5(1/25)=`_____
@[Always] `log_5(1/25)=-2` Because `5^-2=1/5^2=1/25`
a. -2

Type: F
14) `log_7(1/343)=`_____
@[Always] `log_7(1/343)=-3` Because `7^-3=1/7^3=1/343`
a. -3

Type: P
Id: 8341f64b8009404c8cca5beeb1a0a5b8
15) Determine the value for each of the following logarithms. Each of these will have non-integer, fractional answers. (Difficult)

Type: F
16) `log_4 2=`_____
a. 1/2

Type: F
17) `log_4 8=`_____
a. 3/2

Type: F
18) `log_5 (root 3 5)=`_____
a. 1/3

Type: F
19) `log_2 (root 5 4)=`_____
a. 2/5

Type: F
Options: Workspace, Multiple
20) Between what two consecutive integers must the value of `log_4 7342` lie? Justify your answer. _____ and _____
a. 6
b. 7

Type: F
Options: Workspace, Multiple
21) Between what two consecutive integers must the value of `log_5 (1/500)` lie? Justify your answer. _____ and _____
a. -4
b. -3

Type: F, IgnoreCase
Options: Multiple
Score: 10, Partial
22) [HTML]In chemistry, the `pH` of a solution is defined by the equation `pH=-log(H)` where `H` represents the concentration of hydrogen ions in the solution. Any solution with a `pH` less than 7 is considered acidic and any solution with a `pH` greater than 7 is considered basic.Fill in the table below. Round your `pH`’s to the nearest tenth of a unit.<table><tbody><tr><td>Substance</td><td>Concentration of Hydrogen</td><td>pH</td><td>Basic or Acidic?</td></tr><tr><td>Milk</td><td>`1.6xx10^-7`</td><td>____________</td><td>____________</td></tr><tr><td>Coffee</td><td>`1.3xx10^-5`</td><td>____________</td><td>____________</td></tr><tr><td>Bleach</td><td>`2.5xx10^-13`</td><td>____________</td><td>____________</td></tr><tr><td>Lemon Juice</td><td>`7.9xx10^-2`</td><td>____________</td><td>____________</td></tr><tr><td>Rain</td><td>`1.6xx10^-6`</td><td>____________</td><td>____________</td></tr></tbody></table>[/HTML]
@[Always] [Media:4.8-22key.PNG]
[0.1]a. 6.8
[0.1]b. acidic
[0.1]c. 4.9
[0.1]d. acidic
[0.1]e. 12.6
[0.1]f. basic
[0.1]g. 1.1
[0.1]h. acidic
[0.1]i. 5.8
[0.1]j. acidic

Type: E
Score: ExtraCredit
23) Can the value of `log_2 (-4)` be found? What about the value of `log_2 0`? Why or why not? What does this tell you about the domain of `log_b x`?
@[Always] `log_2(-4)` can't be found. It is impossible to find any exponent that we can raise 2 to in order to obtain any negative value (including -2).
`log_2 0` can not be found either, as you can't raise 2 to any power to get a value of 0. This means that `log_bx`'s domain has to be greater than zero,
that is `{x|x>0}`