Question 1

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

Accepted Answer

A)  $\mathrm{c}=\frac{\ln \left(\frac{3 \mathrm{~d}}{2}\right)-8}{5}$ 
B)  $\mathrm{c}=\ln \left(\frac{3 \mathrm{~d}}{2}\right)-\frac{8}{5}$ 
C)  $\mathrm{c}=\frac{\ln \left(\frac{2 \mathrm{~d}}{3}\right)+8}{5}$ 
D)  $\mathrm{c}=\frac{\log \left(\frac{3 \mathrm{~d}}{2}\right)+8}{5}$ 
A)  $\mathrm{c}=\frac{\ln \left(\frac{3 \mathrm{~d}}{2}\right)-8}{5}$ 
B)  $\mathrm{c}=\ln \left(\frac{3 \mathrm{~d}}{2}\right)-\frac{8}{5}$ 
C)  $\mathrm{c}=\frac{\ln \left(\frac{2 \mathrm{~d}}{3}\right)+8}{5}$ 
D)  $\mathrm{c}=\frac{\log \left(\frac{3 \mathrm{~d}}{2}\right)+8}{5}$

Question 2

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

Accepted Answer

A)  $\log 4=0.60205999133 ; 10^{0.60205999133}=4$ 
B)  $\log 0.60205999133=4 ; 10^{4}=0.60205999133$ 
C)  $\log 1.38629436112=4 ; 10^{4}=1.38629436112$ 
D)  $\log 4=1.38629436112 ; 10^{1.38629436112}=4$ 
A)  $\log 4=0.60205999133 ; 10^{0.60205999133}=4$ 
B)  $\log 0.60205999133=4 ; 10^{4}=0.60205999133$ 
C)  $\log 1.38629436112=4 ; 10^{4}=1.38629436112$ 
D)  $\log 4=1.38629436112 ; 10^{1.38629436112}=4$

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $\varnothing$ 
B)  $\frac{3}{2}$ 
C)  - 11 
D)  11 
A)  $\varnothing$ 
B)  $\frac{3}{2}$ 
C)  - 11 
D)  11

Question 5

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 6

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.)

Accepted Answer

A)  5200 years 
B)  1497 years 
C)  2800 years 
D)  3446 years 
A)  5200 years 
B)  1497 years 
C)  2800 years 
D)  3446 years

Question 7

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

Accepted Answer

A)  27 
B)  9 
C)  3 
D)  729 
A)  27 
B)  9 
C)  3 
D)  729

Question 8

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

Accepted Answer

A)  5 
B)  10 
C)  2 
D)  25 
A)  5 
B)  10 
C)  2 
D)  25

Question 9

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

Accepted Answer

A)  32 
B)  2 
C)  5 
D)  -2 
A)  32 
B)  2 
C)  5 
D)  -2

Question 10

Solve the problem.
-A certain noise produces $5.7 \times 10^{-4} \mathrm{watt} / \mathrm{m}^{2}$ of power. What is the decibel level of this noise (to nearest decibel)? Use the formula $\mathrm{D}=10 \log \left(\mathrm{S} / \mathrm{S}_{0}\right)$, where $\mathrm{S}_{0}=10^{-12}$ watt $/ \mathrm{m}^{2}$.

Accepted Answer

A)  88 decibels 
B)  202 decibels 
C)  78 decibels 
D)  9 decibels 
A)  88 decibels 
B)  202 decibels 
C)  78 decibels 
D)  9 decibels

Question 11

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

Accepted Answer

A)  $\ln 3.5=1.2527629685 ; \mathrm{e}^{1.2527629685}=3.5$ 
B)  $\ln 3.5=0.54406804435 ; \mathrm{e}^{0.54406804435}=3.5$ 
C)  $\ln 1.2527629685=3.5 ; \mathrm{e}^{3.5}=1.2527629685$ 
D)  $\ln 0.54406804435=3.5 ; \mathrm{e}^{3.5}=0.54406804435$ 
A)  $\ln 3.5=1.2527629685 ; \mathrm{e}^{1.2527629685}=3.5$ 
B)  $\ln 3.5=0.54406804435 ; \mathrm{e}^{0.54406804435}=3.5$ 
C)  $\ln 1.2527629685=3.5 ; \mathrm{e}^{3.5}=1.2527629685$ 
D)  $\ln 0.54406804435=3.5 ; \mathrm{e}^{3.5}=0.54406804435$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $\frac{11+r}{9}$ 
B)  $\mathrm{e}^{11}+\mathrm{r}$ 
C)  $\frac{\mathrm{e}^{3-r}-8}{9}$ 
D)  $\frac{9}{11+r}$ 
A)  $\frac{11+r}{9}$ 
B)  $\mathrm{e}^{11}+\mathrm{r}$ 
C)  $\frac{\mathrm{e}^{3-r}-8}{9}$ 
D)  $\frac{9}{11+r}$

Question 14

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

Accepted Answer

A)  $\frac{4}{3}$ 
B)  $\frac{5}{4}$ 
C)  $\frac{3}{2}$ 
D)  $\frac{5}{3}$ 
A)  $\frac{4}{3}$ 
B)  $\frac{5}{4}$ 
C)  $\frac{3}{2}$ 
D)  $\frac{5}{3}$

Question 15

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

Accepted Answer

A)  $9=\log _{6561} \frac{1}{4}$ 
B)  $\frac{1}{4}=\log _{6561} 9$ 
C)  $\frac{1}{4}=\log _{9} 6561$ 
D)  $9=\log _{1 / 4} 6561$ 
A)  $9=\log _{6561} \frac{1}{4}$ 
B)  $\frac{1}{4}=\log _{6561} 9$ 
C)  $\frac{1}{4}=\log _{9} 6561$ 
D)  $9=\log _{1 / 4} 6561$

Question 16

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.

Accepted Answer

A)  580 
B)  1182 
C)  1159 
D)  611 
A)  580 
B)  1182 
C)  1159 
D)  611

Question 17

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 years 
A)  11 years 
B)  33 years 
C)  1 year 
D)  5 years

Question 18

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

Accepted Answer

A)  0.393 
B)  1.565 
C)  1.297 
D)  0.565 
A)  0.393 
B)  1.565 
C)  1.297 
D)  0.565

Question 19

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

Accepted Answer

A)  $\log 24 r+\log 6 s$ 
B)  $\log 11+\log r+6 \log s$ 
C)  $24 \log \mathrm{r}+6 \log \mathrm{s}$ 
D)  $\log 8+3 \log r+6 \log s$ 
A)  $\log 24 r+\log 6 s$ 
B)  $\log 11+\log r+6 \log s$ 
C)  $24 \log \mathrm{r}+6 \log \mathrm{s}$ 
D)  $\log 8+3 \log r+6 \log s$

Question 20

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

Accepted Answer

A)  9 
B)  -9 
C)  2 
D)  -2 
A)  9 
B)  -9 
C)  2 
D)  -2

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

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

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

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

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

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.)

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

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

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

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

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

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

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

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

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.

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.)

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

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

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

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Exam 4: Exponential and Logarithmic Functions

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

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

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

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

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

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.)

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

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

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

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

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

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)

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

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

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.