Question 1

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Accepted Answer

A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ E

Question 2

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Accepted Answer

A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ E

Question 3

Sketch the graph of the function. $$g ( x ) = \frac { 1 } { 2 } e ^ { x + 1 }$$

Accepted Answer

A) 
  
B)   
C) 
  
D) 
  
A) 
  
B)   
C) 
  
D) 
  D

Question 4

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Accepted Answer

The answer of Evaluate the expression without using a calculator....

Question 5

Solve the inequality: $0.5 \leq \log x < 2$

Accepted Answer

The answer of Solve the inequality: \(0.5 \leq \log x...

Question 6

Radium - $226$ has a half-life of $1600 \text { years }$) Suppose we have a $300 \mathrm {~g}$
Sample. How much of the sample remains after $200$Years?

Accepted Answer

A)  $105.61 \mathrm {~g}$ 
B)  $124.61 \text { g }$ 
C)  $275.1 \mathrm {~g}$ 
D)  $288.1 \mathrm {~g}$ 
E)  $200.1 \mathrm {~g}$ 
A)  $105.61 \mathrm {~g}$ 
B)  $124.61 \text { g }$ 
C)  $275.1 \mathrm {~g}$ 
D)  $288.1 \mathrm {~g}$ 
E)  $200.1 \mathrm {~g}$

Question 7

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Accepted Answer

A)  $\log \left( \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 } \right)$ 
B)  $\log \left( \frac { \sqrt { x ^ { 2 } - 9 } } { x ^ { 2 } } + 9 \right)$ 
C)  $\log \left( \frac { x ^ { 2 } - 9 } { \sqrt { x ^ { 2 } + 9 } } \right)$ 
D)  $\log \left( \frac { x - 3 } { x + 3 } \right)$ 
E)  $\log \left( \frac { x - 9 } { \sqrt { x + 9 } } \right)$ 
A)  $\log \left( \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 } \right)$ 
B)  $\log \left( \frac { \sqrt { x ^ { 2 } - 9 } } { x ^ { 2 } } + 9 \right)$ 
C)  $\log \left( \frac { x ^ { 2 } - 9 } { \sqrt { x ^ { 2 } + 9 } } \right)$ 
D)  $\log \left( \frac { x - 3 } { x + 3 } \right)$ 
E)  $\log \left( \frac { x - 9 } { \sqrt { x + 9 } } \right)$

Question 8

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Accepted Answer

@#IMG-DLM& 
Domain:

Question 9

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. 
(a) Find a formula for the mass remaining after $t$seconds
b) How much of the sample remains after $200$seconds?
c) After how long will only $20 \mathrm {~g}$ remain?

Accepted Answer

(a) @#LAT-DLM&

b)

Question 10

Sketch the graph of the function. State the domain, range, and asymptote. $f ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Accepted Answer

@#IMG-DLM& 
Domain:

Question 11

Expand the logarithmic expression. $\log \left( \frac { 4 x ^ { 3 } } { y ( x - 2 ) ^ { 6 } } \right)$

Accepted Answer

The answer of Expand the logarithmic expression. \(\log \left( \frac...

Question 12

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ 
. After how many seconds is the velocity 60 ft/s?

Accepted Answer

The answer of The velocity of a sky diver t...

Question 13

Find the domain, range, and asymptote of the function. $g ( x ) = \log _ { 2 } ( x + 4 )$

Accepted Answer

A)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = - 4$ 
B)  Domain: $( 4 , \infty )$
, Range: $( 4 , \infty )$
, Asymptote: $x = 4$ 
C)  Domain: $( - 4 , \infty )$
, Range: $(-\infty, \infty )$
, Asymptote: $x = - 4$ 
D)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = 4$ 
E)  none of these 
A)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = - 4$ 
B)  Domain: $( 4 , \infty )$
, Range: $( 4 , \infty )$
, Asymptote: $x = 4$ 
C)  Domain: $( - 4 , \infty )$
, Range: $(-\infty, \infty )$
, Asymptote: $x = - 4$ 
D)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = 4$ 
E)  none of these

Question 14

Approximately how long will it take an investment of $\$ 900$ to triple, if the interest rate is 3.75% per year compounded continuously?

Accepted Answer

A)  $4.5 \text { years }$ 
B)  $21 \text { years }$ 
C)  $2.9 \text { years }$ 
D)  $29 \text { years }$ 
E)  $9 \text { years }$ 
A)  $4.5 \text { years }$ 
B)  $21 \text { years }$ 
C)  $2.9 \text { years }$ 
D)  $29 \text { years }$ 
E)  $9 \text { years }$

Question 15

How much more intense is an earthquake with a magnitude of $9.5$ 
on the Richter scale than one with a magnitude of $7.6$ ?

Accepted Answer

@#LAT-DLM& 
. So it

Question 16

Expand the logarithmic expression. $\log _ { 5 } \left( \frac { 5 x ^ { 3 } } { y ^ { 3 } ( x - 2 ) ^ { 6 } } \right)$

Accepted Answer

The answer of Expand the logarithmic expression. \(\log _ {...

Question 17

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 2$

Accepted Answer

A)  $0$ 
B)  $4$ 
C)  $3$ 
D)  $1$ 
E)  $2$ 
A)  $0$ 
B)  $4$ 
C)  $3$ 
D)  $1$ 
E)  $2$

Question 18

Solve the equation. Find the exact solution. $3 ^ { 1 - x } = 7$

Accepted Answer

The answer of Solve the equation. Find the exact solution....

Question 19

A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by $t = 3 \frac { \log ( N / 50 ) } { \log 2 }$ 
Find the time required for the colony to grow to two million bacteria.

Accepted Answer

The answer of A certain strain of bacteria divides every...

Question 20

The half-life of a particular radioactive element is 25 days. How long will it take for a 3mg sample to decay to a mass of $1$ 
mg??

Accepted Answer

The answer of The half-life of a particular radioactive element...

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Sketch the graph of the function. $g ( x ) = \frac { 1 } { 2 } e ^ { x + 1 }$

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Solve the inequality: $0.5 \leq \log x < 2$

Radium - $226$ has a half-life of $1600 \text { years }$ ) Suppose we have a $300 \mathrm {~g}$ Sample. How much of the sample remains after $200$ Years?

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. (a) Find a formula for the mass remaining after $t$ seconds b) How much of the sample remains after $200$ seconds? c) After how long will only $20 \mathrm {~g}$ remain?

Sketch the graph of the function. State the domain, range, and asymptote. $f ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Expand the logarithmic expression. $\log \left( \frac { 4 x ^ { 3 } } { y ( x - 2 ) ^ { 6 } } \right)$

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 60 ft/s?

Find the domain, range, and asymptote of the function. $g ( x ) = \log _ { 2 } ( x + 4 )$

Approximately how long will it take an investment of $\$ 900$ to triple, if the interest rate is 3.75% per year compounded continuously?

How much more intense is an earthquake with a magnitude of $9.5$ on the Richter scale than one with a magnitude of $7.6$ ?

Expand the logarithmic expression. $\log _ { 5 } \left( \frac { 5 x ^ { 3 } } { y ^ { 3 } ( x - 2 ) ^ { 6 } } \right)$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 2$

Solve the equation. Find the exact solution. $3 ^ { 1 - x } = 7$

A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by $t = 3 \frac { \log ( N / 50 ) } { \log 2 }$ Find the time required for the colony to grow to two million bacteria.

The half-life of a particular radioactive element is 25 days. How long will it take for a 3mg sample to decay to a mass of $1$ mg??

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 5: Trigonometric Functions: Right Triangle Approach

Combine into a single logarithm. 32ln⁡(x−y)−2ln⁡(x2+y2)\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)23​ln(x−y)−2ln(x2+y2)

Combine into a single logarithm. 32ln⁡(x−y)−2ln⁡(x2+y2)\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)23​ln(x−y)−2ln(x2+y2)

Sketch the graph of the function. g(x)=12ex+1g ( x ) = \frac { 1 } { 2 } e ^ { x + 1 }g(x)=21​ex+1

Evaluate the expression without using a calculator. e2ln⁡8e ^ { 2 \ln 8 }e2ln8

Solve the inequality: 0.5≤log⁡x<20.5 \leq \log x < 20.5≤logx<2

Radium - 226226226 has a half-life of 1600 years 1600 \text { years }1600 years ) Suppose we have a 300 g300 \mathrm {~g}300 g Sample. How much of the sample remains after 200200200 Years?

Combine into a single logarithm. log⁡(x−3)+log⁡(x+3)−12log⁡(x2+9)\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)log(x−3)+log(x+3)−21​log(x2+9)

Graph the function, not by plotting points, but by starting from the graph of y=exy = e ^ { x }y=ex . State the domain, range, and asymptote. h(x)=ex−3+5h ( x ) = e ^ { x - 3 } + 5h(x)=ex−3+5

Radium - 221221221 has a half-life of 30 s30 \mathrm {~s}30 s . Suppose we have a 300 g300 \mathrm {~g}300 g sample. (a) Find a formula for the mass remaining after ttt seconds b) How much of the sample remains after 200200200 seconds? c) After how long will only 20 g20 \mathrm {~g}20 g remain?

Sketch the graph of the function. State the domain, range, and asymptote. f(x)=2+log⁡2(x+4)f ( x ) = 2 + \log _ { 2 } ( x + 4 )f(x)=2+log2​(x+4)

Expand the logarithmic expression. log⁡(4x3y(x−2)6)\log \left( \frac { 4 x ^ { 3 } } { y ( x - 2 ) ^ { 6 } } \right)log(y(x−2)64x3​)

The velocity of a sky diver t seconds after jumping is given by v(t)=80(1−e−02t)v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)v(t)=80(1−e−02t) . After how many seconds is the velocity 60 ft/s?

Find the domain, range, and asymptote of the function. g(x)=log⁡2(x+4)g ( x ) = \log _ { 2 } ( x + 4 )g(x)=log2​(x+4)

Approximately how long will it take an investment of $900\$ 900$900 to triple, if the interest rate is 3.75% per year compounded continuously?

How much more intense is an earthquake with a magnitude of 9.59.59.5 on the Richter scale than one with a magnitude of 7.67.67.6 ?

Expand the logarithmic expression. log⁡5(5x3y3(x−2)6)\log _ { 5 } \left( \frac { 5 x ^ { 3 } } { y ^ { 3 } ( x - 2 ) ^ { 6 } } \right)log5​(y3(x−2)65x3​)

Solve the equation. Find the exact solution. log⁡x+log⁡(x+1)=log⁡2\log x + \log ( x + 1 ) = \log 2logx+log(x+1)=log2

Solve the equation. Find the exact solution. 31−x=73 ^ { 1 - x } = 731−x=7

The half-life of a particular radioactive element is 25 days. How long will it take for a 3mg sample to decay to a mass of 111 mg??

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Sketch the graph of the function. $g ( x ) = \frac { 1 } { 2 } e ^ { x + 1 }$

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Solve the inequality: $0.5 \leq \log x < 2$

Radium - $226$ has a half-life of $1600 \text { years }$ ) Suppose we have a $300 \mathrm {~g}$ Sample. How much of the sample remains after $200$ Years?

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. (a) Find a formula for the mass remaining after $t$ seconds b) How much of the sample remains after $200$ seconds? c) After how long will only $20 \mathrm {~g}$ remain?

Sketch the graph of the function. State the domain, range, and asymptote. $f ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Expand the logarithmic expression. $\log \left( \frac { 4 x ^ { 3 } } { y ( x - 2 ) ^ { 6 } } \right)$

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 60 ft/s?

Find the domain, range, and asymptote of the function. $g ( x ) = \log _ { 2 } ( x + 4 )$

Approximately how long will it take an investment of $\$ 900$ to triple, if the interest rate is 3.75% per year compounded continuously?

How much more intense is an earthquake with a magnitude of $9.5$ on the Richter scale than one with a magnitude of $7.6$ ?

Expand the logarithmic expression. $\log _ { 5 } \left( \frac { 5 x ^ { 3 } } { y ^ { 3 } ( x - 2 ) ^ { 6 } } \right)$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 2$

Solve the equation. Find the exact solution. $3 ^ { 1 - x } = 7$

The half-life of a particular radioactive element is 25 days. How long will it take for a 3mg sample to decay to a mass of $1$ mg??