Answers CMS 2026-2027 NC Math 4 INITIAL CREDITLogarithmic Functions

Logarithmic Functions — Test Answers

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Which equation is represented by the graph?

y is equal to natural log x minus 3

y is equal to e to the x th power minus 3

y is equal to e to the x th power minus 4

y is equal to natural log x minus 4

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

all real numbers greater than negative 1

all real numbers less than negative 1

all real numbers greater than 1

all real numbers less than 1

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

0 point 5 5 7

1 point 7 9 6

0 point 2 3 3

0 point 6 2 0

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

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).

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Four curves are plotted, with two entirely above the x-axis and two entirely below the x-axis. Above the x-axis, one curve extends from an arrow on the y-axis at 0 comma 0.5 up to an upward-pointing arrow near 1 comma 5, and a second curve extends from an upward-pointing arrow near 1 comma 5 down to an arrow near 5 comma 0.5. Below the x-axis, one curve extends from an arrow on the y-axis at 0 comma negative 0.5 down to a downward-pointing arrow near 1 comma negative 5, and a second curve extends from a downward-pointing arrow near 1 comma negative 5 up to an arrow near 5 comma negative 0.5.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Two curves intersect at 1 comma 0. The first curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0 and 3 comma 1, and continues increasing to an arrow near 5 comma 1.5. The second curve extends from an upward-pointing arrow near 0 comma 5, decreases downward to pass through 1 comma 0 and 2 comma negative 1, and continues decreasing to an arrow near 5 comma negative 2.5

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. A straight line extends from a downward-pointing arrow near negative 5 comma negative 5, passes through 0 comma 0, and continues upward to an arrow near 5 comma 5. A curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0, and continues increasing to an arrow near 5 comma 1.5.

If you are given the graph of h of x is equal to the log base 6 of x , how could you graph m times x is equal to log sub 6 of open paren x plus 3 close paren ?

Translate each point of the graph of h x 3 units down.

Translate each point of the graph of h x 3 units up.

Translate each point of the graph of h x 3 units right.

Translate each point of the graph of h x 3 units left.

The magnitude, cap m , of an earthquake is defined to be cap m is equal to the log of cap i over cap s , where cap i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and cap s is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

1 point 5

negative 0 point 5

negative 1 point 5

3 point 6

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

x is equal to 1 over 12

x is equal to 9

x is equal to 3

x is equal to 3 halves

What is the range of the function y is equal to e raised to the 4 x power ?

y is less than 4

y is less than 0

y is greater than 0

y is greater than 4

What is the true solution to the given equation? 2 log sub 3 6 x minus log sub 3 of 4 x is equal to 2 log sub 3 open paren x plus 2 close paren

x is equal to negative 2 and x is equal to 1

x is equal to 2 and x is equal to 4

x is equal to negative 2 and x is equal to 2

x is equal to 1 and x is equal to 4

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 ?

x is equal to 4

x is equal to negative 2

x is equal to negative 4

x is equal to 8

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 ?

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

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

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

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

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

negative 1 fourth

1 fourth

negative 4

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

x is equal to 8

x is equal to 2

x is equal to 4

x is equal to 64

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

16 thirds

1 third

An equation for the depreciation of a car is given by y is equal to cap A times open paren 1 minus r close paren to the t th power , where y is equal to current value of the car, cap A is equal to original cost, r is equal to rate of depreciation, and t is equal to time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10 percent Approximately how old is the car?

5 point 6 years

3 point 3 years

5 point 0 years

6 point 6 years

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

all real numbers less than 3

all real numbers less than negative 3

all real numbers greater than 3

all real numbers greater than negative 3

The loudness, cap l , measured in decibels (Db), of a sound intensity, cap i , measured in watts per square meter, is defined as cap l is equal to 10 log the fraction with numerator cap i and denominator cap i sub 0 , where cap i sub 0 is equal to 10 to the negative 12 power and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10 inverse ?

2 Db

110 Db

22 Db

60 Db

What is the solution to the equation 2 raised to the x plus 4 power minus 12 is equal to 20 ?

x is equal to 1

x is equal to 0

x is equal to 9

x is equal to 2

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

b is greater than 0 and b is equal to 1

b is less than 0 and b is not equal to 1

b is greater than 0 and b is not equal to 1

b is less than 0 and b is equal to 1

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 ?

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

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

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

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

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Logarithmic Functions — Test Answers

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