AnswersAlgebra IIExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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Which equation is represented by the graph?

A
y is equal to e to the x th power minus 3
B
y is equal to e to the x th power minus 4
C
y is equal to natural log x minus 3
D
y is equal to natural log x minus 4
2
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What is the solution to the equation 2 raised to the x plus 4 power minus 12 is equal to 20 ?

A
x is equal to 2
B
x is equal to 1
C
x is equal to 9
D
x is equal to 0
3

What is the solution to log sub 5 of open paren x plus 30 close paren is equal to 3 ?

A
x is equal to negative 5
B
x is equal to 95
C
x is equal to negative 95
D
x is equal to 5
4

How does the value of log_2⁡100 compare with the value of the log base 6 of 20 ?

A
The value of the log base 2 of 100 is about 3 times the value of the log base 6 of 20 .
B
The value of the log base 2 of 100 is about 1 fourth times the value of the log base 6 of 20 .
C
The value of the log base 2 of 100 is about 4 times the value of ​​​​​​​ the log base 6 of 20 .
D
The value of the log base 2 of 100 is about 1 third times the value of the log base 6 of 20 .
5

For what value of n does the fraction with numerator 216 raised to the n minus 2 power and denominator open paren 1 over 36 close paren raised to the 3 n power is equal to 216 ?

A
5 ninths
B
1
C
negative 3
D
negative 1 third
6

What is the approximate value of the log base 6 of 25 ?

A
0 point 6 2 0
B
0 point 5 5 7
C
1 point 7 9 6
D
0 point 2 3 3
7

Which of the following is true about the base b of a logarithmic function?

A
b is greater than 0 and b is not equal to 1
B
b is less than 0 and b is equal to 1
C
b is greater than 0 and b is equal to 1
D
b is less than 0 and b is not equal to 1
8

What is the solution of log sub 2 of open paren 3 x minus 7 close paren is equal to 3 ?

A
4
B
5
C
1 third
D
16 thirds
9

What is the range of the function y is equal to 2 e to the x th power minus 1 ?

A
all real numbers greater than 1
B
all real numbers less than negative 1
C
all real numbers greater than negative 1
D
all real numbers less than 1
10

What is the solution to the given equation? log sub 6 4 x squared minus the log base 6 of x is equal to 2

A
x is equal to 1 over 12
B
x is equal to 9
C
x is equal to 3
D
x is equal to 3 halves
11

Which graph shows the solution to the equation? the log base 3 of x is equal to the log base 0 point 5 of x

A
Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. There are two hyperbolas defined for positive values of x. One of the parabola has vertex (3 comma 0) and it approaches the x axis and the line x equals 1. The other hyperbola has vertex at (2 comma negative 1) and it approaches the x axis and the line x equals 1.
B
Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. There is a curved graph that passes through (negative 4 comma negative 2), and (negative 2 comma negative 1). It increases in the third quadrant, changes direction at the origin, and then again increases in the first quadrant passing through (5 comma 1 point 5). There is line that passes through the origin, (1 comma 1), and (2 comma 2).
C
Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. Two curves are drawn. One of the curve approaches the y axis in the first quadrant and passes through (2 comma negative 1) and (4 comma negative 2). The other curve passes through (3 comma 1), (1 comma 0), and approaches y axis in the fourth quadrant.
D
Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. There is a smooth curve that passes through (0 point 5 comma negative 1), and (1 comma 0), and approaches y axis in the fourth quadrant. There is a line that passes through the origin, (1 comma 1), and (2 comma 2).
12

Calvin deposits 400 dollars in a savings account that accrues 5 percent interest compounded monthly. After c years, Calvin has 658 point 8 0 dollars Makayla deposits 300 dollars in a different savings account that accrues 6 percent interest compounded quarterly. After m years, Makayla has 613 point 0 4 dollars What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Makayla invests her money 1 year longer.
B
Calvin invests his money 2 years longer.
C
Makayla invests her money 2 years longer.
D
Calvin invests his money 1 year longer.
13

What is the true solution to the equation? the natural log of e raised to the natural log x power plus the natural log of e raised to the the natural log of x squared power is equal to 2 ln 8

A
x is equal to 64
B
x is equal to 8
C
x is equal to 2
D
x is equal to 4
14

Which expression is equivalent to log sub w the fraction with numerator open paren x squared minus 6 close paren to the 4th power and denominator cube root of x squared plus 8 ?

A
4 log sub w the fraction with numerator x squared and denominator 1296 minus 1 third log sub w open paren 2 x plus 8 close paren
B
4 times open paren log sub w x squared minus 1 third log sub w open paren x squared plus 8 close paren minus 6 close paren
C
4 log sub w open paren x squared minus 6 close paren minus 1 third log sub w open paren x squared plus 8 close paren
D
4 log sub w open paren x squared minus 6 close paren minus 3 log sub w open paren x squared plus 8 close paren
15

Which of the following shows the extraneous solution to the logarithmic equation? log sub 3 of open paren 18 x cubed close paren minus log sub 3 of 2 x is equal to the log base 3 of 144

A
x is equal to negative 2
B
x is equal to negative 4
C
x is equal to negative 16
D
x is equal to negative 8
16

What is the value of the log base 625 of 5 ?

A
negative 4
B
negative 1 fourth
C
1 fourth
D
4
17

Which expression is equivalent to log sub 12 the fraction with numerator x to the 4th power square root of x cubed minus 2 end root and denominator open paren x plus 1 close paren to the 5th power ?

A
4 log sub 12 x plus 1 half log sub 12 the fraction with numerator x cubed and denominator 2 minus 5 log sub 12 x plus the log base 12 of 1
B
4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x times 1 close paren
C
the log base the log base 12 of 4 of x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 x plus 1
D
4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x plus 1 close paren
18

For what value of n does open paren 1 over 36 close paren to the n th power is equal to 216 ?

A
negative 3 halves
B
3 halves
C
negative 3
D
3
19

What is the solution to 2 log sub 9 x is equal to log sub 9 8 plus log sub 9 of open paren x minus 2 close paren ?

A
x is equal to negative 2
B
x is equal to 4
C
x is equal to 8
D
x is equal to negative 4
20

The range of which function is open paren 2 comma infinity close paren ?

A
y is equal to 5 to the x th power plus 2
B
y is equal to 2 times open paren 5 to the x th power close paren
C
y is equal to 2 to the x th power
D
y is equal to 5 raised to the x plus 2 power

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