Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Solving Logarithmic Equations using Technology

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The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

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

b > 0 and b = 1

b > 0 and

b < 0 and

b < 0 and b = 1

For what value of n does ?

–3

Negative one-third

Five-ninths

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and 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.

–1.5

–0.5

1.5

3.6

–1.5

–0.5

1.5

3.6

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

Which graph represents an exponential decay function?

On a coordinate plane, a curve opens up and to the right in quadrant 4.

On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.

On a coordinate plane, a line slightly curves up in quadrant 1.

On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.

If the equation below is solved by graphing, which statement is true?

The curves intersect at approximately x = 0.46.

The curves intersect at approximately x = 0.75.

The curves intersect at approximately x = 1.11.

The curves intersect at approximately x = 3.07.

What is the simplified value of the exponential expression ?

Option

Which graph shows the solution to the equation below?

On a coordinate plane, 2 curves intersect at (1, 0).

On a coordinate plane, a line intersects with a curve.

On a coordinate plane, a line with positive slope and a curve are shown.

On a coordinate plane, 2 hyperbolas are shown.

Which function is shown in the graph below?

y = (one-half) Superscript x + 3 Baseline minus 1

y = (one-half) Superscript x minus 3 Baseline + 1

y = (one-half) Superscript x minus 1 Baseline + 3

y = (one-half) Superscript x + 1 Baseline minus 3

What is the approximate value of ?

0.233

0.557

0.620

1.796

For what value of n does ?

–3

Negative three-halves

Three-halves

For what value of n does ?

–3

Negative one-third

Five-ninths

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

b > 0 and b = 1

b > 0 and

b < 0 and

b < 0 and b = 1

For what value of x does ?

–9

–3

Which is equivalent to ?

192

Which is the graph of ?

On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.

On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.

On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.

On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.

How does the value of compare with the value of ?

The value of is about 4 times the value of .

The value of is about times the value of .

The value of is about 3 times the value of .

The value of is about times the value of .

What is the value of ?

–4

Negative one-fourth

One-fourth

What is the domain of ?

all real numbers less than –3

all real numbers greater than –3

all real numbers less than 3

all real numbers greater than 3

What is the solution of log2 (3x - 7) = 3?

One-third

Sixteen-thirds

What is the approximate value of ?

0.233

0.557

0.620

1.796

If , what is the value of s?

–1

no solution

Which of the following shows the graph of y = 4x + 3?

On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.

For what value of n does ?

–3

Negative three-halves

Three-halves

For what value of x does ?

–9

–3

How does the value of compare with the value of ?

The value of is about 4 times the value of .

The value of is about times the value of .

The value of is about 3 times the value of .

The value of is about times the value of .

If , what is the value of s?

–1

no solution

If the equation below is solved by graphing, which statement is true?

The curves intersect at approximately x = 0.46.

The curves intersect at approximately x = 0.75.

The curves intersect at approximately x = 1.11.

The curves intersect at approximately x = 3.07.

What is the domain of ?

all real numbers less than –3

all real numbers greater than –3

all real numbers less than 3

all real numbers greater than 3

Which graph shows the solution to the equation below?

On a coordinate plane, 2 curves intersect at (1, 0).

On a coordinate plane, a line intersects with a curve.

On a coordinate plane, a line with positive slope and a curve are shown.

On a coordinate plane, 2 hyperbolas are shown.

Which function is shown in the graph below?

y = (one-half) Superscript x + 3 Baseline minus 1

y = (one-half) Superscript x minus 3 Baseline + 1

y = (one-half) Superscript x minus 1 Baseline + 3

y = (one-half) Superscript x + 1 Baseline minus 3

Which is the graph of ?

On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.

On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.

On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.

On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.

Which of the following shows the graph of y = 4x + 3?

On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.

If you are given the graph of , how could you graph ?

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

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

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

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

If you are given the graph of , how could you graph ?

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

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

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 range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

What is the value of ?

Which equation is equivalent to ?

3 squared = left-bracket log Subscript 3 Baseline (x + 5) right-bracket cubed

2 cubed = left-bracket log Subscript 3 Baseline (x + 5) right-bracket squared

3 squared = x + 5

2 cubed = x + 5

When simplified, the expression is 12. Which is a possible value of x?

144

256

Which is equivalent to ?

What is the value of ?

–4

Negative one-fourth

One-fourth

For what value of a does ?

–1

no solution

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