Quiz about Alg2 Unit 2B REVIEW: Exponential and Logarithmic Functions

Question 1

Write the following scenario using this equation: $$A=Pe^{rt}$$ .

Tony invested $2000 into an account with a 4.5% annual interest rate, compounding continuously.

Accepted Answer

$$A=2000e^{\left(.045\right)\left(t\right)}$$

Answer

$$2000=Pe^{\left(.045\right)\left(t\right)}$$

Answer

$$A=2000e^{\left(.45\right)\left(t\right)}$$ .

Question 2

Write the following in exponential form:

$$\log_3\left(x\right)=7$$

Accepted Answer

$$3^7=x$$

Answer

$$7^3=x$$

Answer

$$3^x=7$$

Question 3

Write the following in exponential form:

$$\ln\left(3\right)=x$$

Accepted Answer

$$e^x=3$$

Answer

$$3^x=e$$

Answer

$$3^x=3$$

Question 4

For the graph to the right, The solid line is $$y=\log_4\left(x\right)$$ . What would be the equation of the transformed dashed graph?

Accepted Answer

$$y=\log_4\left(x+4\right)+4$$

Answer

$$y=\log_4\left(x-4\right)+4$$

Answer

$$y=\log_4\left(x\right)-4$$

Question 5

Write the following in exponential form:

log (x)=3 =

Accepted Answer

$$10^3=x$$

Answer

$$x^3=10$$

Answer

$$3^{10}=x$$

Question 6

Write the following as a logarithm: $$4^x=16384$$

Accepted Answer

$$\log_4\left(16384\right)\ =\ x$$

Answer

$$\log_x\left(16384\right)\ =4$$

Answer

$$\log_{16384}\left(x\right)=4$$

Question 7

For the graph to the left, identify the domain and range.

Accepted Answer

Domain: $$\left(-4,\infty\right)$$

Range: $$\left(-\infty,\infty\right)$$

Answer

Domain: $$\left(-\infty,\infty\right)$$

Range: $$\left(-4,\infty\right)$$

Answer

Domain: $$\left(4,\infty\right)$$

Range: $$\left(\infty,-\infty\right)$$

Question 8

Find the inverse: $$y=\ln\left(4x\right)-7$$

Accepted Answer

$$y=\frac{e^{\left(x+7\right)}}{4}$$

Answer

$$y=e^x+7$$

Answer

$$y=4e^{\left(x+7\right)}$$

Question 9

Write the following as a logarithm:

$$e^x=20.085$$

Accepted Answer

$$\ln\left(20.085\right)=x$$

Answer

$$\ln x=20.085$$

Answer

ln (20.085)=e

Question 10

Write the following as a logarithm:

$$26=x^3$$

Accepted Answer

$$\log_x26=3$$

Answer

$$\log_3x=26$$

Answer

$$\log3=x$$

Question 11

Example: Tony invested $2000 into an account with a 4.5% annual interest rate, compounding continuously.

How much will Tony have after 6 years? : $$A=2000e^{.045t}$$

Accepted Answer

$2619.93

Answer

$29759.46

Answer

$2045.00

Question 12

Solve the following equation for x:

$$3^{\left(2x+1\right)}=3^{\left(x-9\right)}$$

Accepted Answer

x = -10

Answer

x = 5

Answer

x = 8

Answer

x = 10

Question 13

Solve the following equation for x:

$$\log\left(2x+6\right)=\log\left(4x+2\right)$$

Accepted Answer

x = 2

Answer

x = 4

Answer

x = -2

Answer

x = -4

Question 14

Solve the following equation for x:

$$e^{\left(x+1\right)}-4=12$$

Accepted Answer

x = ln(16) - 1

Answer

x = ln(16)

Answer

x = ln(15) - 1

Answer

x = ln(15)

Question 15

Solve for x:

$$\log\left(3x\right)=24$$

Accepted Answer

$$\frac{10^{24}}{3}=x$$

Answer

$$\frac{24}{3}=x$$

Answer

$$\frac{\log24}{3}=x$$

Answer

$$24^3=x$$

Question 16

Solve for x:

$$\log_4\left(x+2\right)-3=2$$

Accepted Answer

$$4^5-2=x$$

Answer

$$5^4+2=x$$

Answer

$$4^5+2=x$$

Question 17

Expand $$\ln\left(xy^3\right)$$

Accepted Answer

$$\ln x+3\ln y$$

Answer

$$\ln x-3\ln y$$

Answer

$$3\ln x+\ln y$$

Question 18

Expand $$\log\left(\frac{10x^2}{w^3}\right)$$

Accepted Answer

$$\log\ 10+2\log x-3\log w$$

Answer

$$\log10-2\log x+3\log w$$

Answer

$$2\log10+\log x-3\log\ w$$

Question 19

Condense the following:

$$\frac{1}{2}\log x-5\log y$$

Accepted Answer

$$\log\left(\frac{x^{\frac{1}{2}}}{y^5}\right)$$

Answer

$$\log\left(\frac{x^2}{y^5}\right)$$

Answer

$$\log\left(x^{\frac{1}{2}}y^{\left(5\right)}\right)$$

Alg2 Unit 2B REVIEW: Exponential and Logarithmic Functions

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