Solve the equation log 9 x + log 9 ( x - 24)= 2.

A) x = 29 B) x = -3 C) x = 27 D) x = 3 E) x = 729 A) x = 29 B) x = -3 C) x = 27 D) x = 3 E) x = 729

Write 10 6 = 1,000,000 in logarithmic form. For example, 2 3 = 8 becomes log 2 8 = 3 in logarithmic form.

A) log 10 6 = 1,000,000 B) log 6 1,000,000 = 10 C) log 1,000,000 10 = 6 D) log 1,000,000 6 = 10 E) log 10 1,000,000 = 6 A) log 10 6 = 1,000,000 B) log 6 1,000,000 = 10 C) log 1,000,000 10 = 6 D) log 1,000,000 6 = 10 E) log 10 1,000,000 = 6

Write 2 9 = 512 in logarithmic form. For example, 2 3 = 8 becomes log 2 8 = 3 in logarithmic form.

A) log 2 9 = 512 B) log 512 2 = 9 C) log 512 9 = 2 D) log 2 512 = 9 E) log 9 512 = 2 A) log 2 9 = 512 B) log 512 2 = 9 C) log 512 9 = 2 D) log 2 512 = 9 E) log 9 512 = 2

Solve the equation log 3 x + log 32 = 2.

A) x = 18 B) x = 5.5 C) x = 4.5 D) x = 5 E) x = 4 A) x = 18 B) x = 5.5 C) x = 4.5 D) x = 5 E) x = 4

Exam 11: Exponential and Logarithmic Functions

Suppose that in a certain culture, the equation $\mathcal { Q } ( t ) = 900 e ^ { 0.5 t }$ expresses the number of bacteria present as a function of the time t , where t is expressed in hours. How many bacteria are present at the end of 2 hours? The choices are rounded to the nearest whole.

(Multiple Choice)

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Question 21

Use the change of base formula to identify the expression that is equivalent to $\log _ { 9 } 7$ .

(Multiple Choice)

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Question 22

Solve the equation. $\log _ { \frac { 2 } { 3 } } \frac { n } { p } = 5$

(Multiple Choice)

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Question 23

Solve the equation log₉ x + log₉ ( x - 24)= 2.

(Multiple Choice)

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Question 24

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { \pi } e$

(Short Answer)

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Question 25

How long will it take $700 to double itself if it is invested at 13% interest compounded semiannually? Please round the answer to the nearest tenth.

(Multiple Choice)

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Question 26

Graph the exponential function. f ( x )= e ^x - 5

(Multiple Choice)

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Question 27

Write 10⁶ = 1,000,000 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

(Multiple Choice)

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Question 28

Solve the equation. $\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 625 } { 256 }$

(Multiple Choice)

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Question 29

An earthquake has a period of $\frac { 1 } { 2 }$ second, and an amplitude of $500,000$ micrometers. Find its measure on the Richter scale.

(Multiple Choice)

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Question 30

Solve the logarithmic equation. Check the solution. $\log _ { 2 } x = \log _ { 2 } \frac { 1 } { x } + 6$

(Multiple Choice)

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Question 31

Graph the function. $f ( x ) = \frac { e ^ { x } + e ^ { - x } } { 5 }$

(Multiple Choice)

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Question 32

Graph the function $y = 3 + \log _ { 2 } x$ . Remember that the graph of $f ( x ) = \log _ { 2 } x$ is given. $Graph the function y = 3 + \log _ { 2 } x . Remember that the graph of f ( x ) = \log _ { 2 } x is given.$

(Multiple Choice)

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Question 33

Write 2⁹ = 512 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

(Multiple Choice)

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Question 34

Suppose that the present population of a city is 550,000. Use the equation P ( t )= 550,000 e^{0.034 t} to estimate future growth. Estimate the population 50 years from now.

(Multiple Choice)

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Question 35

Solve the equation log₃ x + log₃2 = 2.

(Multiple Choice)

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Question 36

Graph the exponential function. f ( x )= 3 ^x ^{+ 2}

(Multiple Choice)

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Question 37

Evaluate the following. $\log _ { 8 } 8 ^ { 6 }$

(Multiple Choice)

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Question 38

The number of grams Q of a certain radioactive substance present after t seconds is given by the equation $Q = 7,000 e ^ { - 0.1 t }$ . How many grams remain after 17 seconds? Please round the answers to the nearest whole.

(Multiple Choice)

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Question 39

Solve the equation. $10 ^ { x } = 0.01$

(Multiple Choice)

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Question 40

Suppose that in a certain culture, the equation $\mathcal { Q } ( t ) = 900 e ^ { 0.5 t }$ expresses the number of bacteria present as a function of the time t , where t is expressed in hours. How many bacteria are present at the end of 2 hours? The choices are rounded to the nearest whole.

Use the change of base formula to identify the expression that is equivalent to $\log _ { 9 } 7$ .

Solve the equation. $\log _ { \frac { 2 } { 3 } } \frac { n } { p } = 5$

Solve the equation log₉ x + log₉ ( x - 24)= 2.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { \pi } e$

How long will it take $700 to double itself if it is invested at 13% interest compounded semiannually? Please round the answer to the nearest tenth.

Graph the exponential function. f ( x )= e ^x - 5

Write 10⁶ = 1,000,000 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

Solve the equation. $\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 625 } { 256 }$

An earthquake has a period of $\frac { 1 } { 2 }$ second, and an amplitude of $500,000$ micrometers. Find its measure on the Richter scale.

Solve the logarithmic equation. Check the solution. $\log _ { 2 } x = \log _ { 2 } \frac { 1 } { x } + 6$

Graph the function. $f ( x ) = \frac { e ^ { x } + e ^ { - x } } { 5 }$

Graph the function $y = 3 + \log _ { 2 } x$ . Remember that the graph of $f ( x ) = \log _ { 2 } x$ is given. $Graph the function y = 3 + \log _ { 2 } x . Remember that the graph of f ( x ) = \log _ { 2 } x is given.$

Write 2⁹ = 512 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

Suppose that the present population of a city is 550,000. Use the equation P ( t )= 550,000 e^{0.034 t} to estimate future growth. Estimate the population 50 years from now.

Solve the equation log₃ x + log₃2 = 2.

Graph the exponential function. f ( x )= 3 ^x ^{+ 2}

Evaluate the following. $\log _ { 8 } 8 ^ { 6 }$

The number of grams Q of a certain radioactive substance present after t seconds is given by the equation $Q = 7,000 e ^ { - 0.1 t }$ . How many grams remain after 17 seconds? Please round the answers to the nearest whole.

Solve the equation. $10 ^ { x } = 0.01$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Filters

Exam 11: Exponential and Logarithmic Functions

Use the change of base formula to identify the expression that is equivalent to log⁡97\log _ { 9 } 7log9​7 .

Solve the equation. log⁡23np=5\log _ { \frac { 2 } { 3 } } \frac { n } { p } = 5log32​​pn​=5

Solve the equation log 9 x + log 9 ( x - 24)= 2.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. log⁡πe\log _ { \pi } elogπ​e

How long will it take $700 to double itself if it is invested at 13% interest compounded semiannually? Please round the answer to the nearest tenth.

Graph the exponential function. f ( x )= e x - 5

Write 10 6 = 1,000,000 in logarithmic form. For example, 2 3 = 8 becomes log 2 8 = 3 in logarithmic form.

Solve the equation. (45)x=625256\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 625 } { 256 }(54​)x=256625​

An earthquake has a period of 12\frac { 1 } { 2 }21​ second, and an amplitude of 500,000500,000500,000 micrometers. Find its measure on the Richter scale.

Solve the logarithmic equation. Check the solution. log⁡2x=log⁡21x+6\log _ { 2 } x = \log _ { 2 } \frac { 1 } { x } + 6log2​x=log2​x1​+6

Graph the function. f(x)=ex+e−x5f ( x ) = \frac { e ^ { x } + e ^ { - x } } { 5 }f(x)=5ex+e−x​

Graph the function y=3+log⁡2xy = 3 + \log _ { 2 } xy=3+log2​x . Remember that the graph of f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x is given.

Write 2 9 = 512 in logarithmic form. For example, 2 3 = 8 becomes log 2 8 = 3 in logarithmic form.

Suppose that the present population of a city is 550,000. Use the equation P ( t )= 550,000 e 0.034 t to estimate future growth. Estimate the population 50 years from now.

Solve the equation log 3 x + log 32 = 2.

Graph the exponential function. f ( x )= 3 x + 2

Evaluate the following. log⁡886\log _ { 8 } 8 ^ { 6 }log8​86

The number of grams Q of a certain radioactive substance present after t seconds is given by the equation Q=7,000e−0.1tQ = 7,000 e ^ { - 0.1 t }Q=7,000e−0.1t . How many grams remain after 17 seconds? Please round the answers to the nearest whole.

Solve the equation. 10x=0.0110 ^ { x } = 0.0110x=0.01

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Filters

Use the change of base formula to identify the expression that is equivalent to $\log _ { 9 } 7$ .

Solve the equation. $\log _ { \frac { 2 } { 3 } } \frac { n } { p } = 5$

Solve the equation log₉ x + log₉ ( x - 24)= 2.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { \pi } e$

Graph the exponential function. f ( x )= e ^x - 5

Write 10⁶ = 1,000,000 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

Solve the equation. $\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 625 } { 256 }$

An earthquake has a period of $\frac { 1 } { 2 }$ second, and an amplitude of $500,000$ micrometers. Find its measure on the Richter scale.

Solve the logarithmic equation. Check the solution. $\log _ { 2 } x = \log _ { 2 } \frac { 1 } { x } + 6$

Graph the function. $f ( x ) = \frac { e ^ { x } + e ^ { - x } } { 5 }$

Graph the function $y = 3 + \log _ { 2 } x$ . Remember that the graph of $f ( x ) = \log _ { 2 } x$ is given. $Graph the function y = 3 + \log _ { 2 } x . Remember that the graph of f ( x ) = \log _ { 2 } x is given.$

Write 2⁹ = 512 in logarithmic form. For example, 2³ = 8 becomes log₂ 8 = 3 in logarithmic form.

Suppose that the present population of a city is 550,000. Use the equation P ( t )= 550,000 e^{0.034 t} to estimate future growth. Estimate the population 50 years from now.

Solve the equation log₃ x + log₃2 = 2.

Graph the exponential function. f ( x )= 3 ^x ^{+ 2}

Evaluate the following. $\log _ { 8 } 8 ^ { 6 }$

The number of grams Q of a certain radioactive substance present after t seconds is given by the equation $Q = 7,000 e ^ { - 0.1 t }$ . How many grams remain after 17 seconds? Please round the answers to the nearest whole.

Solve the equation. $10 ^ { x } = 0.01$