Algebra 2 B - Unit 2: Exponential and Logarithmic Functions, Part 2

examine the graph of the logarithmic function f(x). https://cdstools.flipswitch.com/asset/media/1239305 the function f(x) has a vertical asymptote at x= [𝖻𝗅𝖺𝗇𝗄]

3

if 7^6x-11 = 7^2x+1, what is the value of x?

3

9^2x = 27

3/4

100^4x = 1000

3/8

solve for x. 3^5x+7 = 3^7x-1

4

solve for x. 5^2x-5 = 125

4

which expression is equivalent to log_4 x^5?

5 log_4 x

a nearby pond has 5 frogs, and the population doubles every year. which inequality, where t is the number of years, models when the population of frogs will be greater than 75?

5(2)^t>75

solve the equation for x. 5^x/2=65 round your answer to three places.

5.187

use the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239309 what is the x-intercept?

(-2,0)

examine the function f(x)=log_2x. which point is the intersection of f(x) and the line y=1?

(2,1)

which is the x-intercept of f(x)=log_6(2x)-1?

(3,0)

Lesson 6

Exponential Equations

Lesson 9

Exponentials in Context

Lesson 8

How to Solve Exponential Equations with Technology

Lesson 10

Key Features of Logarithmic Functions

The graph shows preimage f(x) and image g(x)=f(x)+k https://cdstools.flipswitch.com/asset/media/1239620 What is the value of k?

-4

on the first day of a social media ad campaign, a website had 15 unique visitors. over the following several days, the website received three times the number of unique visitors as the previous day. which equation can be used to determine the number of unique visitors, v, that the website would have on day d of the ad campaign?

v=15⋅3^(d−1)

solve for x. 4^3x = 4^x-1

x = -1/2

5^-2x-9 = 5^4x+15

x = -4

16^3x = 64

x = 1/2

solve the equation for x. 4 * 2^x = 32

x = 3

128 = 2^3x-5

x = 4

solve for x. 64 = 2^2x-4

x = 5

solve 9^4x = 243 for x.

x = 5/8

e^2x = 4

x = ln 4 / 2

8 * e^x-1 = 56

x = ln 7 + 1

10^3x = 12

x = log 12 / 3

2^4x = 6

x = log_2 6 / 4

which expression is equivalent to log_2 6^x?

x log_2 6

otto wants to graph the function f(x)=log_2x. he begins by analyzing the function and recording the following items: 1. x-intercept of f(x) 2. vertical asymptote of f(x) 3. intersection of f(x) and the line y=1 which answer correctly shows what otto should conclude about f(x)?

x-intercept: (1,0) vertical asymptote: x=0 intersection of f(x) and y=1: (2,1)

the membership fee at a sports club was $600 per year. each year, the membership fee increased by 7%. the cost of membership, y, can be modeled by the equation y=600(1.07)^x, where x is the number of years. how many years will it take for the cost of the membership to be $900? choose the answer that gives the correct logarithmic equation and answer.

x=log_1.07(1.5)≈6

solve 6^3x+1=10.8 for x. which answer shows the correct steps?

x≈0.109

solve the equation for x. 8^x+2=99.6

x≈0.213

If 4^3x=37.9 what is the value of x?

x≈0.874

solve 25^2x-1=400 for x. which answer shows the correct steps?

x≈1.431

solve the equation for x. 2^x/3=100.6

x≈19.96

if 3^x/4+2=56.8, what is the value of x?

x≈6.708

if 3^(x/2)+4=7.32, what is the value of x?

x≈−4.38

the membership fee at a sports club was $600 per year. each year, the membership fee increased by 7%. which equation models the cost of the membership fee, y, after x years?

y=600(1.07)^x

examine the function f(x)=log_3x. which point is the intersection of f(x) and the line y=1?

(3,1)

use the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239308 where does f(x) and the line y=1 intersect?

(3,1)

use the graph of the logarithmic function f(x)f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239323 where does f(x) and the line y=1 intersect?

(4,1)

The graph shows preimage f(x) and image g(x)=f(x)+k. https://cdstools.flipswitch.com/asset/media/1239620 What is the value of k?

-4

examine the graph of the logarithmic function f(x). https://cdstools.flipswitch.com/asset/media/1239320 the function f(x) has a vertical asymptote at x= [𝖻𝗅𝖺𝗇𝗄]

-4

examine the logarithmic function f(x). f(x)=log_1/3x the function f(x) has a vertical asymptote at x= [𝖻𝗅𝖺𝗇𝗄].

0

examine the logarithmic function f(x): f(x)=log_5x-2 the function f(x) has a vertical asymptote at x= [𝖻𝗅𝖺𝗇𝗄]

0

what is the value of log_17 2?

0.24

if 6^4x=82, what is the value of x?

0.615

which interval contains all the x-values where f(x)=log_0.75x is positive?

0<x<1

which interval represents all of the x-values where f(x)=log_2/5x is positive?

0<x<1

what is the value of log_27 165?

1.549

which expression is equivalent to log_3 24^2?

2 log_3 24

if 17^2x-3=35, what is the value of x? round your answer to three places.

2.127

what is the value of log_6 49?

2.17

what is the value of log_5 75?

2.68

8^7x-5 = 8^4x-3

2/3

use the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239310 which interval contains all the x-values where f(x) is positive?

2<x<3

on the first day of a social media ad campaign, a website had 15 unique visitors. over the following several days, the website received three times the number of unique visitors as the previous day. The number of visitors, v, can be modeled by v=15⋅3^(d−1), where d is the number of days in the campaign. on which day of the ad campaign did the website have 10,000 visitors?

7

Lesson 11

Transformations of Logarithmic Functions

user the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239322 which statements describe the end behavior of f(x)? select two answers.

as x approaches 2.5, y approaches ∞ as x approaches ∞, y approaches -∞

use the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239307 which statements describe the end behavior of f(x)? select two answers.

as x approaches −1, y approaches −∞. as x approaches ∞, y approaches ∞.

consider the following function: f(x)=log_2/3x which statements describe the end behavior of f(x)? select two statements.

as x approaches ∞, y approaches −∞. as x approaches 0, y approaches ∞.

use the graph of logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239321 what is the domain and range of the function? match the domain and range with the corresponding set of points.

domain: (0,∞) range: (-∞,∞)

use the graph of the logarithmic function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239306 what are the domain and range of the function? match the domain and range with the corresponding set of points.

domain: (−2,∞) range: (−∞,∞)

The function f(x)=log_5(x+2) is reflected to get g(x)=−f(x). What is the effect on f(x)?

f(x) is reflected over the x-axis.

The function f(x)=log_4(x) is dilated to become g(x)=f(1/3x). What is the effect on f(x)?

f(x) is stretched horizontally by a factor of 3.

the function f(x)=log(x+2) is translated to get g(x)=log(x-2). what is the effect on f(x)?

f(x) moves 4 units to the right.

the function f(x)=log_1/3(x+1) is translated to get g(x)=log_1/3(x-4). what is the effect on f(x)?

f(x) moves 5 units downward.

The graph shows a translation of the preimage f(x)=log_1/2(x) to become g(x). https://cdstools.flipswitch.com/asset/media/1239622 What is the function rule for g(x)?

g(x)=-3log_1/2(x)

use the graph of the logarithmic function g(x) to answer the question. https://cdstools.flipswitch.com/asset/media/1239315 which function represents the graph?

g(x)=log_2x

The graph shows a translation of the preimage f(x)=log_5(x+1) to become g(x). https://cdstools.flipswitch.com/asset/media/1239621 Which is the transformation rule and the function rule for g(x)?

g(x)=log_5(x−2)+4 g(x)=f(x−2)+3

examine the following function: f(x)=log_3x which graph represents the function?

https://cdstools.flipswitch.com/asset/media/1239311

examine the following function: h(x)=log_1/2x which graph represents the function?

https://cdstools.flipswitch.com/asset/media/1239316

examine the following function: f(x)=log_1/4x which graph represent the function?

https://cdstools.flipswitch.com/asset/media/1239324

the function is translated from f(x)=log_3(x) to g(x)=f(x)+4. which graph shows f(x) and its translation g(x)?

https://cdstools.flipswitch.com/asset/media/1239600

which graph shows f(x)=log_2(x-1) to g(x)=f(x-3)

https://cdstools.flipswitch.com/asset/media/1239604

A function, f(x), is transformed to be g(x)=2⋅f(x). Which graph correctly demonstrates this transformation, where f(x) is the preimage and g(x) is the image?

https://cdstools.flipswitch.com/asset/media/1239608

Which graph shows f(x)=log_0.25(x+1) and the dilation g(x)=−3f(x)?

https://cdstools.flipswitch.com/asset/media/1239612

Which graph shows f(x)=log_3(x) and the dilation g(x)=f(−1/2x)?

https://cdstools.flipswitch.com/asset/media/1239616

which expressions are equivalent to log_9 14?

ln 14/ln 9 log 14/log 9

match each logarithm with its equivalent expression.

log_7 y^10 : 10 log_7 y ln 7^10 = 10 ln 7 log 7^4 : 4 log 7

lesson 7

properties of logarithms

a nearby pond has 5 frogs, and the population doubles every year. the inequality 5(2)^t>75, where t is the number of years, models when the population of frogs will be greater than 75. based on the inequality, when will the population of frogs in the pond be greater than 75?

t>4