AnswersAlgebra IIExponential and Logarithmic Functions

Practice Test Answers

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What is the solution to the log base the log base 4 of 8 of x is equal to 3 ?

A
x is equal to 8
B
x is equal to 3 eighths
C
x is equal to 3 halves
D
x is equal to 2
2
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What is the range of y is equal to log sub 2 of open paren x minus 6 close paren ?

A
all real numbers
B
all real numbers not equal to 0
C
all real number greater than 6
D
all real numbers less than 6
3

What is the range of the function f of x is equal to negative 2 times open paren 6 to the x th power close paren plus 3 ?

A
left parenthesis negative infinity comma negative 2 right bracket
B
open paren negative infinity comma 3 close paren
C
left bracket negative 2 comma infinity right parenthesis
D
left bracket 3 comma infinity right parenthesis
4

Which of the following shows the true solution to the logarithmic equation solved? log sub 2 of x plus log sub 2 of open paren x plus 7 close paren is equal to 3 log sub 2 of open bracket x times open paren x plus 7 close paren close bracket is equal to 3 x times open paren x plus 7 close paren is equal to 2 cubed x squared plus 7 x minus 8 is equal to 0 open paren x plus 8 close paren times open paren x minus 1 close paren is equal to 0 x is equal to negative 8 comma 1

A
x is equal to 1
B
x is equal to 1 and x is equal to negative 8
C
x is equal to negative 8
D
x is equal to 1 and x is equal to 8
5

What are the domain and range of f of x is equal to the log of open paren x minus 1 close paren plus 2 ?

A
domain: x is greater than 1 ; range: y is greater than 2
B
domain: all real numbers; range: all real numbers
C
domain: x is greater than 1 ; range: all real numbers
D
domain : all real numbers; range: y is greater than 1
6

Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

A
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).
B
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma negative 1).
C
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the y axis in the fourth quadrant. It passes through the points (1 comma 0), (3 comma 1) and increases as x increases. There is a line is parallel to the x axis and cuts the y axis at (0 comma negative 1).
D
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).
7

Two different radioactive isotopes decay to 10 percent of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

A
33 days
B
3 days
C
13 days
D
10 days
8

The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?

A
32
B
320
C
15
D
737
9

What is the solution of the natural log of open paren x plus 6 close paren minus natural log 9 is equal to 2 ? Round your answer to the nearest hundredth.

A
x is equal to 60 point 5 0
B
x is equal to 66 point 5 0
C
x is equal to 53 point 5 0
D
x is equal to 72 point 5 0
10

What are the solutions to log sub 6 of open paren x squared plus 8 close paren is equal to 1 plus log sub 6 of x ?

A
x is equal to 2 and x is equal to 4
B
x is equal to negative 2 and x is equal to negative 4
C
x is equal to 1 and x is equal to negative 8
D
x is equal to negative 1 and x is equal to 8
11

Which function has a horizontal asymptote of y is equal to 3 ?

A
f of x is equal to 2 times 4 raised to the x minus 3 power
B
f of x is equal to 3 times open paren 2 to the x th power close paren
C
f of x is equal to 2 times open paren 4 to the x th power close paren plus 3
D
f of x is equal to 2 times open paren 3 to the x th power close paren
12

What is the solution of the log base x of 729 is equal to 3 ?

A
6
B
9
C
81
D
18
13

One brand of vinegar has a pH of 4 point 5 Another brand has a pH of 5 point 0 The equation for the pH of a substance is pH is equal to negative log times open bracket cap h raised to the plus power close bracket , where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A
3 point 2 times 10 inverse
B
6 point 8 times 10 to the 4th power
C
2 point 2 times 10 to the negative 5 power
D
3 point 2 times 10 to the 1th power
14

The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?

A
320
B
32
C
15
D
737

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