AnswersMathematics IIIExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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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 open paren x squared minus 6 close paren minus 3 log sub w open paren x squared plus 8 close paren
B
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
C
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
D
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
2
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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 5
C
x is equal to negative 95
D
x is equal to 95
3

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
5

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

Which graph represents an exponential decay function?

A
Image with description On a coordinate plane, the curve passes through (negative 3 comma 8), (negative 2 comma 4), (negative 1 comma 2), and (0 comma 1). It approaches to the x-axis as the value of x increases.
B
Image with description On a coordinate plane, the curve originate on y-axis and passes through (1 comma 1), (4 comma 2),and (8 comma 3) in the first quadrant.
C
Image with description On a coordinate plane, the curve passes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8). It approaches to the x-axis as the value of x decreases.
D
Image with description On a coordinate plane, the curve originate on y-axis and passes through (1 comma negative 1) and (4 comma negative 2) in the fourth quadrant.
9

What is the domain of y is equal to log sub 4 of open paren x plus 3 close paren ?

A
all real numbers greater than negative 3
B
all real numbers less than negative 3
C
all real numbers greater than 3
D
all real numbers less than 3
12

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 greater than 0 and b is equal to 1
C
b is less than 0 and b is equal to 1
D
b is less than 0 and b is not equal to 1
13

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 1 third 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 3 times the value of the log base 6 of 20 .
14

Which geometric series converges?

A
1 plus 1 half plus 1 fourth plus 1 eighth plus dot dot dot
B
the sum from n is equal to 1 to infinity of 7
C
1 over 81 plus 1 over 27 plus 1 ninth plus 1 third plus dot dot dot
D
the sum from n is equal to 1 to infinity of 1 fifth
15

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 0
C
x is equal to 1
D
x is equal to 9
16

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

A
0 point 2 3 3
B
0 point 5 5 7
C
1 point 7 9 6
D
0 point 6 2 0
17

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

A
y is equal to 2 to the x th power
B
y is equal to 5 raised to the x plus 2 power
C
y is equal to 2 times open paren 5 to the x th power close paren
D
y is equal to 5 to the x th power plus 2
19

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 negative 1
B
all real numbers greater than 1
C
all real numbers less than 1
D
all real numbers less than negative 1
20

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
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
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
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
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

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