AnswersMathematics IIIExponential and Logarithmic Functions

Practice Test Answers

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1
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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 3 comma infinity right parenthesis
D
left bracket negative 2 comma infinity right parenthesis
2
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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 3 eighths
B
x is equal to 2
C
x is equal to 8
D
x is equal to 3 halves
3

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
4

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 Coordinate plane with x-axis and y-axis. A logarithmic-shaped curve begins near the y-axis at x equals 0 and extends to the right. The curve passes through 1 comma 0, rises gradually through approximately 3 comma 1 and 9 comma 2, and continues increasing as x increases. A horizontal line y equals negative 1 extends across the graph with arrows on both ends. The curve intersects the horizontal line near 0.3 comma negative 1 and lies above the line for x values greater than this point. Both the curve and the horizontal line continue indefinitely as indicated by arrows.
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 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 negative 1).
5

The two expressions have the same value when rounded to the nearest hundredth. the log base 5 of b the log base 9 of 48 What is the approximate value of log b to the nearest hundredth?

A
9 point 1 6
B
65 point 5 3
C
1 point 2 3
D
0 point 9 3
6

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
8 fifths
B
2
C
5 eighths
D
8
7

Which geometric series diverges?

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

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
13 days
C
10 days
D
3 days
9

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

A
the log base 2 of x plus 3 log sub 2 9
B
3 log sub 2 x minus the log base 2 of 9
C
the log base 2 of 9 plus 3 log sub 2 x
D
3 log sub 2 9 minus the log base 2 of x
10

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

A
e log sub 6 f
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
f log sub 6 e
11

Which fraction represents the decimal 0 point 8 8 8 8 dot dot dot ?

A
the fraction with numerator 1 comma 111 and denominator 1 comma 250
B
8 ninths
C
80 over 99
D
9 eighths
12

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 72 point 5 0
B
x is equal to 60 point 5 0
C
x is equal to 53 point 5 0
D
x is equal to 66 point 5 0
13

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: all real numbers; range: all real numbers
B
domain: x is greater than 1 ; range: all real numbers
C
domain : all real numbers; range: y is greater than 1
D
domain: x is greater than 1 ; range: y is greater than 2
14

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

A
4
B
1
C
5
D
2
15

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 less than 6
C
all real number greater than 6
D
all real numbers not equal to 0
16

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

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

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