Question 1

Find the value of the expression.
- log⁡9181\log 9 \frac{1}{81}log9811​

Accepted Answer

A)   9
B)   -9
C)   2
D)   -2 E) A) and C)
F) B) and C)

Question 2

Solve the exponential equation.
- 2(10−2x) =642^{(10-2 x) }=642(10−2x) =64

Accepted Answer

A)   32
B)   2
C)   5
D)   -2 E) C) and D)
F) B) and C)

Question 3

Solve the equation for  ccc .}
- 2e5c+8=3 d2 \mathrm{e}^{5 \mathrm{c}+8}=3 \mathrm{~d}2e5c+8=3 d

Accepted Answer

A)    c=ln⁡(3 d2) −85\mathrm{c}=\frac{\ln \left(\frac{3 \mathrm{~d}}{2}\right) -8}{5}c=5ln(23 d​) −8​ 
B)    c=ln⁡(3 d2) −85\mathrm{c}=\ln \left(\frac{3 \mathrm{~d}}{2}\right) -\frac{8}{5}c=ln(23 d​) −58​ 
C)    c=ln⁡(2 d3) +85\mathrm{c}=\frac{\ln \left(\frac{2 \mathrm{~d}}{3}\right) +8}{5}c=5ln(32 d​) +8​ 
D)    c=log⁡(3 d2) +85\mathrm{c}=\frac{\log \left(\frac{3 \mathrm{~d}}{2}\right) +8}{5}c=5log(23 d​) +8​E) None of the above
F) A) and C)

Question 4

Graph the function.
- f(x) =4(4x−2) f(x) =4^{(4 x-2) }f(x) =4(4x−2)

Accepted Answer

A)    
B)    
C)    
D)    E) None of the above
F) All of the above

Question 5

Find the value of the expression.
- log⁡525\log _{5} 25log5​25

Accepted Answer

A)   5
B)   10
C)   2
D)   25 E) A) and C)
F) A) and B)

Question 6

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
- log⁡8r3 s6\log 8 \mathrm{r}^{3} \mathrm{~s}^{6}log8r3 s6

Accepted Answer

A)    log⁡24r+log⁡6s\log 24 r+\log 6 slog24r+log6s 
B)    log⁡11+log⁡r+6log⁡s\log 11+\log r+6 \log slog11+logr+6logs 
C)    24log⁡r+6log⁡s24 \log \mathrm{r}+6 \log \mathrm{s}24logr+6logs 
D)    log⁡8+3log⁡r+6log⁡s\log 8+3 \log r+6 \log slog8+3logr+6logsE) A) and D)
F) None of the above

Question 7

Graph the function.
- f(x) =e3x−4f(x) =e^{3 x}-4f(x) =e3x−4

Accepted Answer

A)    
B)    
C)    
D)    E) A) and D)
F) B) and C)

Question 8

Solve the equation for  sss .
- 3−r=ln⁡(9 s+8) 3-\mathrm{r}=\ln (9 \mathrm{~s}+8) 3−r=ln(9 s+8)

Accepted Answer

A)    11+r9\frac{11+r}{9}911+r​ 
B)    e11+r\mathrm{e}^{11}+\mathrm{r}e11+r 
C)    e3−r−89\frac{\mathrm{e}^{3-r}-8}{9}9e3−r−8​ 
D)    911+r\frac{9}{11+r}11+r9​E) A) and D)
F) All of the above

Question 9

Provide an appropriate response.
-How can you use the change-of-base rule for logarithms to help solve the equation 5 = 3x?

Accepted Answer

The equation you've provided seems to co...

Question 10

Solve the problem.
-The growth in the population of a certain rodent at a dump site fits the exponential function  A(t) =599e0.02tA(t) =599 e^{0.02 t}A(t) =599e0.02t , where  ttt  is the number of years since 1967. Estimate the population in the year 2000.

Accepted Answer

A)   580
B)   1182
C)   1159
D)   611 E) All of the above
F) None of the above

Question 11

Find the value of the expression.
- log⁡832\log _{8} 32log8​32

Accepted Answer

A)    43\frac{4}{3}34​ 
B)    54\frac{5}{4}45​ 
C)    32\frac{3}{2}23​ 
D)    53\frac{5}{3}35​E) B) and C)
F) B) and D)

Question 12

Solve the equation.
- 72x=3x+17^{2 x}=3^{x+1}72x=3x+1

Accepted Answer

A)   0.393
B)   1.565
C)   1.297
D)   0.565 E) C) and D)
F) B) and D)

Question 13

Solve the equation.
- log⁡(3+x) −log⁡(x−4) =log⁡2\log (3+x) -\log (x-4) =\log 2log(3+x) −log(x−4) =log2

Accepted Answer

A)    ∅\varnothing∅ 
B)    32\frac{3}{2}23​ 
C)   - 11
D)   11 E) B) and D)
F) All of the above

Question 14

Solve the problem.
-How long will it take for the population of a certain country to double if its annual growth rate is 6.1? (Round to the nearest year.)

Accepted Answer

A)   11 years
B)   33 years
C)   1 year
D)   5 yearsE) C) and D)
F) B) and C)

Question 15

Solve the problem.
-An artifact is discovered at a certain site. If it has  65%65 \%65%  of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of  0.0125%0.0125 \%0.0125%  annually.)

Accepted Answer

A)   5200 years
B)   1497 years
C)   2800 years
D)   3446 years E) B) and C)
F) None of the above

Question 16

Solve the problem.
-A certain noise produces  5.7×10−4watt/m25.7 	imes 10^{-4} \mathrm{watt} / \mathrm{m}^{2}5.7×10−4watt/m2  of power. What is the decibel level of this noise (to nearest decibel) ? Use the formula  D=10log⁡(S/S0) \mathrm{D}=10 \log \left(\mathrm{S} / \mathrm{S}_{0}ight) D=10log(S/S0​)  , where  S0=10−12\mathrm{S}_{0}=10^{-12}S0​=10−12  watt  /m2/ \mathrm{m}^{2}/m2 .

Accepted Answer

A)   88 decibels
B)   202 decibels
C)   78 decibels
D)   9 decibels E) A) and B)
F) C) and D)

Question 17

Write the logarithmic and exponential equations associated with the display.
- g(x) =ln⁡xg(x) =\ln xg(x) =lnx

Accepted Answer

A)    ln⁡3.5=1.2527629685;e1.2527629685=3.5\ln 3.5=1.2527629685 ; \mathrm{e}^{1.2527629685}=3.5ln3.5=1.2527629685;e1.2527629685=3.5 
B)    ln⁡3.5=0.54406804435;e0.54406804435=3.5\ln 3.5=0.54406804435 ; \mathrm{e}^{0.54406804435}=3.5ln3.5=0.54406804435;e0.54406804435=3.5 
C)    ln⁡1.2527629685=3.5;e3.5=1.2527629685\ln 1.2527629685=3.5 ; \mathrm{e}^{3.5}=1.2527629685ln1.2527629685=3.5;e3.5=1.2527629685 
D)    ln⁡0.54406804435=3.5;e3.5=0.54406804435\ln 0.54406804435=3.5 ; \mathrm{e}^{3.5}=0.54406804435ln0.54406804435=3.5;e3.5=0.54406804435E) None of the above
F) B) and C)

Question 18

Write in logarithmic form.
- 65611/4=96561^{1 / 4}=965611/4=9

Accepted Answer

A)    9=log⁡6561149=\log _{6561} \frac{1}{4}9=log6561​41​ 
B)    14=log⁡65619\frac{1}{4}=\log _{6561} 941​=log6561​9 
C)    14=log⁡96561\frac{1}{4}=\log _{9} 656141​=log9​6561 
D)    9=log⁡1/465619=\log _{1 / 4} 65619=log1/4​6561E) All of the above
F) B) and D)

Question 19

Find the value of the expression.
- log⁡993\log _{9} 9^{3}log9​93

Accepted Answer

A)   27
B)   9
C)   3
D)   729 E) B) and C)
F) A) and B)

Question 20

Write the logarithmic and exponential equations associated with the display.
- f(x) =log⁡xf(x) =\log xf(x) =logx

Accepted Answer

A)    log⁡4=0.60205999133;100.60205999133=4\log 4=0.60205999133 ; 10^{0.60205999133}=4log4=0.60205999133;100.60205999133=4 
B)    log⁡0.60205999133=4;104=0.60205999133\log 0.60205999133=4 ; 10^{4}=0.60205999133log0.60205999133=4;104=0.60205999133 
C)    log⁡1.38629436112=4;104=1.38629436112\log 1.38629436112=4 ; 10^{4}=1.38629436112log1.38629436112=4;104=1.38629436112 
D)    log⁡4=1.38629436112;101.38629436112=4\log 4=1.38629436112 ; 10^{1.38629436112}=4log4=1.38629436112;101.38629436112=4E) A) and C)
F) C) and D)

Exam 4: Exponential and Logarithmic Functions

Find the value of the expression. - $\log _{8} 32$

Correct Answer
verified

Solve the exponential equation. - $2^{(10-2 x) }=64$

Correct Answer
verified

Correct Answer
verified

Solve the equation for $c$ .} - $2 \mathrm{e}^{5 \mathrm{c}+8}=3 \mathrm{~d}$

Correct Answer
verified

Graph the function. - $f(x) =4^{(4 x-2) }$ $Graph the function. - f(x) =4^{(4 x-2) } A) B) C) D)$

Correct Answer
verified

Solve the problem. -How long will it take for the population of a certain country to double if its annual growth rate is 6.1? (Round to the nearest year.)

Correct Answer
verified

Solve the equation for $s$ . - $3-\mathrm{r}=\ln (9 \mathrm{~s}+8)$

Correct Answer
verified

Solve the problem. -The growth in the population of a certain rodent at a dump site fits the exponential function $A(t) =599 e^{0.02 t}$ , where $t$ is the number of years since 1967. Estimate the population in the year 2000.

Correct Answer
verified

Correct Answer
verified

Write in logarithmic form. - $6561^{1 / 4}=9$

Correct Answer
verified

Find the value of the expression. - $\log _{5} 25$

Correct Answer
verified

Correct Answer
verified

Provide an appropriate response. -How can you use the change-of-base rule for logarithms to help solve the equation 5 = 3^x?

Correct Answer
Answered by ExamLex AI
The equation you've provided seems to co...
View Answer

Find the value of the expression. - $\log 9 \frac{1}{81}$

Correct Answer
verified

Solve the equation. - $7^{2 x}=3^{x+1}$

Correct Answer
verified

Graph the function. - $f(x) =e^{3 x}-4$ $Graph the function. - f(x) =e^{3 x}-4 A) B) C) D)$

Correct Answer
verified

Find the value of the expression. - $\log _{9} 9^{3}$

Correct Answer
verified

Solve the problem. -An artifact is discovered at a certain site. If it has $65 \%$ of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of $0.0125 \%$ annually.)

Correct Answer
verified

Solve the equation. - $\log (3+x) -\log (x-4) =\log 2$

Correct Answer
verified

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\log 8 \mathrm{r}^{3} \mathrm{~s}^{6}$

Correct Answer
verified

Exam 4: Exponential and Logarithmic Functions

Find the value of the expression. - log⁡832\log _{8} 32log8​32

Correct AnswerverifiedShow Answer

Solve the exponential equation. - 2(10−2x) =642^{(10-2 x) }=642(10−2x) =64

Correct AnswerverifiedShow Answer

Write the logarithmic and exponential equations associated with the display. - g(x) =ln⁡xg(x) =\ln xg(x) =lnx

Correct AnswerverifiedShow Answer

Solve the equation for ccc .} - 2e5c+8=3 d2 \mathrm{e}^{5 \mathrm{c}+8}=3 \mathrm{~d}2e5c+8=3 d

Correct AnswerverifiedShow Answer

Graph the function. - f(x) =4(4x−2) f(x) =4^{(4 x-2) }f(x) =4(4x−2)

Correct AnswerverifiedShow Answer

Solve the problem. -How long will it take for the population of a certain country to double if its annual growth rate is 6.1? (Round to the nearest year.)

Correct AnswerverifiedShow Answer

Solve the equation for sss . - 3−r=ln⁡(9 s+8) 3-\mathrm{r}=\ln (9 \mathrm{~s}+8) 3−r=ln(9 s+8)

Correct AnswerverifiedShow Answer

Solve the problem. -The growth in the population of a certain rodent at a dump site fits the exponential function A(t) =599e0.02tA(t) =599 e^{0.02 t}A(t) =599e0.02t , where ttt is the number of years since 1967. Estimate the population in the year 2000.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Write in logarithmic form. - 65611/4=96561^{1 / 4}=965611/4=9

Correct AnswerverifiedShow Answer

Find the value of the expression. - log⁡525\log _{5} 25log5​25

Correct AnswerverifiedShow Answer

Write the logarithmic and exponential equations associated with the display. - f(x) =log⁡xf(x) =\log xf(x) =logx

Correct AnswerverifiedShow Answer

Provide an appropriate response. -How can you use the change-of-base rule for logarithms to help solve the equation 5 = 3x?

Correct AnswerAnswered by ExamLex AIThe equation you've provided seems to co...View AnswerShow Answer

Find the value of the expression. - log⁡9181\log 9 \frac{1}{81}log9811​

Correct AnswerverifiedShow Answer

Solve the equation. - 72x=3x+17^{2 x}=3^{x+1}72x=3x+1

Correct AnswerverifiedShow Answer

Graph the function. - f(x) =e3x−4f(x) =e^{3 x}-4f(x) =e3x−4

Correct AnswerverifiedShow Answer

Find the value of the expression. - log⁡993\log _{9} 9^{3}log9​93

Correct AnswerverifiedShow Answer

Solve the problem. -An artifact is discovered at a certain site. If it has 65%65 \%65% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125%0.0125 \%0.0125% annually.)

Correct AnswerverifiedShow Answer

Solve the equation. - log⁡(3+x) −log⁡(x−4) =log⁡2\log (3+x) -\log (x-4) =\log 2log(3+x) −log(x−4) =log2

Correct AnswerverifiedShow Answer

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - log⁡8r3 s6\log 8 \mathrm{r}^{3} \mathrm{~s}^{6}log8r3 s6

Correct AnswerverifiedShow Answer

Find the value of the expression. - $\log _{8} 32$

Correct Answer
verified

Solve the exponential equation. - $2^{(10-2 x) }=64$

Correct Answer
verified

Correct Answer
verified

Solve the equation for $c$ .} - $2 \mathrm{e}^{5 \mathrm{c}+8}=3 \mathrm{~d}$

Correct Answer
verified

Graph the function. - $f(x) =4^{(4 x-2) }$ $Graph the function. - f(x) =4^{(4 x-2) } A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Solve the equation for $s$ . - $3-\mathrm{r}=\ln (9 \mathrm{~s}+8)$

Correct Answer
verified

Solve the problem. -The growth in the population of a certain rodent at a dump site fits the exponential function $A(t) =599 e^{0.02 t}$ , where $t$ is the number of years since 1967. Estimate the population in the year 2000.

Correct Answer
verified

Correct Answer
verified

Write in logarithmic form. - $6561^{1 / 4}=9$

Correct Answer
verified

Find the value of the expression. - $\log _{5} 25$

Correct Answer
verified

Correct Answer
verified

Provide an appropriate response. -How can you use the change-of-base rule for logarithms to help solve the equation 5 = 3^x?

Correct Answer
Answered by ExamLex AI
The equation you've provided seems to co...
View Answer

Find the value of the expression. - $\log 9 \frac{1}{81}$

Correct Answer
verified

Solve the equation. - $7^{2 x}=3^{x+1}$

Correct Answer
verified

Graph the function. - $f(x) =e^{3 x}-4$ $Graph the function. - f(x) =e^{3 x}-4 A) B) C) D)$

Correct Answer
verified

Find the value of the expression. - $\log _{9} 9^{3}$

Correct Answer
verified

Solve the problem. -An artifact is discovered at a certain site. If it has $65 \%$ of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of $0.0125 \%$ annually.)

Correct Answer
verified

Solve the equation. - $\log (3+x) -\log (x-4) =\log 2$

Correct Answer
verified

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\log 8 \mathrm{r}^{3} \mathrm{~s}^{6}$

Correct Answer
verified