AnswersMathematics IIIExponential and Logarithmic Functions

Practice Test Answers

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1
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What is the range of the function y is equal to e to the x th power plus 1 graphed?

A
y is greater than 1
B
y is greater than 0
C
y is less than 0
D
y is less than 1
2
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If 343 to the x th power is equal to 49 raised to the 4 minus x power , what is the value of x ?

A
5 eighths
B
2
C
8 fifths
D
8
3

Which geometric series diverges?

A
the sum from n is equal to 1 to infinity of negative 12
B
the sum from n is equal to 1 to infinity of 2 thirds
C
3 fifths plus 3 tenths plus 3 over 20 plus 3 over 40 plus dot dot dot
D
negative 10 plus 4 minus 8 fifths plus 16 over 25 minus dot dot dot
4

For what value of x does 625 is equal to 5 raised to the 6 minus 2 x power ?

A
1
B
5
C
4
D
2
5

What is the range of y is equal to log sub 2 of open paren x minus 6 close paren ?

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

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 2
B
x is equal to 3 eighths
C
x is equal to 8
D
x is equal to 3 halves
7

For what value of x does 625 is equal to 5 raised to the 6 minus 2 x power ?

A
5
B
1
C
2
D
4
8

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: y is greater than 1
C
domain: all real numbers; range: all real numbers
D
domain: x is greater than 1 ; range: all real numbers
9

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 1 and x is equal to negative 8
B
x is equal to negative 2 and x is equal to negative 4
C
x is equal to 2 and x is equal to 4
D
x is equal to negative 1 and x is equal to 8
10

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

A
f of x is equal to 2 times open paren 3 to the x th power close paren
B
f of x is equal to 2 times 4 raised to the x minus 3 power
C
f of x is equal to 3 times open paren 2 to the x th power close paren
D
f of x is equal to 2 times open paren 4 to the x th power close paren plus 3
11

Which expression is equivalent to log sub 2 9 x cubed ?

A
3 log sub 2 9 minus the log base 2 of x
B
the log base 2 of x plus 3 log sub 2 9
C
3 log sub 2 x minus the log base 2 of 9
D
the log base 2 of 9 plus 3 log sub 2 x
12

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
737
C
320
D
15
13

What is log sub 6 e to the f th power rewritten using the power property?

A
f log sub 6 e
B
log sub 6 of open paren e plus f close paren
C
log sub 6 of open paren e times f close paren
D
e log sub 6 f
14

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 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).
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), (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).
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 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).
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).
15

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
13 days
B
33 days
C
10 days
D
3 days
16

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
left bracket negative 2 comma infinity right parenthesis
C
open paren negative infinity comma 3 close paren
D
left bracket 3 comma infinity right parenthesis
17

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

A
81
B
6
C
9
D
18
18

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 66 point 5 0
B
x is equal to 53 point 5 0
C
x is equal to 60 point 5 0
D
x is equal to 72 point 5 0
19

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
2 point 2 times 10 to the negative 5 power
B
6 point 8 times 10 to the 4th power
C
3 point 2 times 10 inverse
D
3 point 2 times 10 to the 1th power
20

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

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