Unit 7 Review (Algebra 2)

Unit 7 (Logarithms) Review

​Algebra 2

Sections in Unit 7

• 7.1 Intro to Exponential Growth/Decay

• 7.2 Graphing Exponential Functions

• 7.3 Intro to the Natural Base, e

• 7.4 Solving Exponential Equations (Common Bases)

• 7.5 Intro to Logs

• *7.6 Graphing Logs* (Skipped)

• 7.7 Properties of Logs

• 7.8 Solving Log Equations

• 7.9 Logarithm Applications

• 7.10 Solving Using Change of Base

Multiple Choice

Given the function $$y=3\left(0.95\right)^x$$ , what is the rate of decay?

• 95%

• 5%

• .95%

• .05%

Multiple Choice

Rewrite $$\log_{81}27=\frac{3}{4}$$ into exponential form.

• $$27^{81}=\frac{4}{3}$$

• $$81^3=27^4$$

• $$27^{\frac{4}{3}}=81$$

• $$81^{\frac{3}{4}}=27$$

Multiple Choice

Rewrite $$3^x=13$$ into logarithmic form.

• $$\log_{13}x=3$$

• $$\log_313=x$$

• $$\log_3x=13$$

• $$\log_x13=3$$

Multiple Choice

$$\log_2\left(3x\right)-\log_2\left(3\right)=\ ?$$

• $$\log_2\left(3x-3\right)$$

• $$\log_2x$$

• $$\log_29x$$

• $$\log_x2$$

Fill in the Blanks

Solve for x.

$\log_7\left(4x-9\right)=\log_7\left(3x+1\right)$

x =

?

Multiple Choice

$$\log_4\left(x^7\right)=\ ?$$

• $$7\log_4x$$

• $$\log_47x$$

• $$\log_{28}x$$

• $$7+\log_4x$$

Multiple Choice

Compared to the parent in blue, how has the graph of the shown exponential been transformed?

• down 2

• left 2

• up 2

• right 2

Multiple Choice

What is the equation of the solid red graph's asymptote?

• y = 1/2

• y = 0

• x = 2

• y = 2

Multiple Choice

What two whole numbers does the expression $$\log_597$$ fall between?

• 0 and 1

• 1 and 2

• 2 and 3

• 3 and 4

Multiple Select

Which of the following functions represent exponential DECAY?

Select ALL that apply.

• $$y=3\cdot\left(\frac{1}{2}\right)^x+1$$

• $$y=\frac{1}{3}\left(1.92\right)^x-3$$

• $$y=3e^{-.73x}+100$$

Fill in the Blanks

Evaluate. If necessary, round to 3 decimal places, or if necessary, write "undefined".

$3\log_416\ =\ ?$

Fill in the Blanks

Evaluate. If necessary, round to 3 decimal places, or if necessary, write "undefined".

$\log_719\ =\ ?$

Fill in the Blanks

Evaluate. If necessary, round to 3 decimal places, or if necessary, write "und".

$\log_2\left(-7\right)$

Fill in the Blanks

Solve the following. Type your answer as a decimal.

$\left(\frac{1}{25}\right)^x=125^{x-3}$

Fill in the Blanks

Solve the following. Find the exact answer, but type in any solution to 3 decimal places. If no solution exists, type "ns".

$4^x=12$

x =

?

Fill in the Blanks

Solve the following. Find the exact answer, but type in any solution to 3 decimal places. If no solution exists, type "ns".

$7+\ln\left(5x-1\right)=19$

x =

?

Fill in the Blanks

Solve the following. Find the exact answer, but type in any solution to 3 decimal places. If no solution exists, type "ns".

$\log_4x+\log_4\left(x-2\right)=\log_415$

x =

?

Fill in the Blanks

Suppose you invest $1,500 into an account that earns 2.6% annual interest, compounded continuously. How much will you have in your account in 6 years? Round to the nearest cent.

$

?

Fill in the Blanks

You deposit $9000 into bank account paying 3% interest, compounded continuously. How long will it take for your account to reach $17000? Round to the nearest whole year.

years

​That's it!

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• You can retry the practice version as much as you want!

• Be sure to to the review packet too!