Algebra 2 Unit 4: Exponential and Logarithmic Functions

Logarithms and their properties, solving exponential and log equations, compound and continuous interest, and inverses. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Evaluating logarithmsNo calculator

Evaluate $\log_2 32$.

1. $\frac{1}{5}$
2. $6$
3. $5$
4. $16$

Question 2

Exponential and log formNo calculator

Which equation is $3^4=81$ written in logarithmic form?

1. $\log_{3} 4=81$
2. $\log_{4} 81=3$
3. $\log_{81} 3=4$
4. $\log_{3} 81=4$

Question 3

Logarithmic equationsNo calculator

Solve $\log_5(x-2)=2$.

1. $x=25$
2. $x=12$
3. $x=27$
4. $x=7$

Question 4

Properties of logarithmsNo calculator

Which expression equals $\log\left(\frac{x^3y}{z}\right)$ for positive $x$, $y$ and $z$?

1. $\log 3x+\log y-\log z$
2. $3\log x\cdot\log y-\log z$
3. $3\log x+\log y+\log z$
4. $3\log x+\log y-\log z$

Question 5

Exponential equationsCalculator

Solve $4^x=20$. Give your answer to the nearest hundredth.

1. $0.46$
2. $2.16$
3. $2.17$
4. $5.00$

Question 6

Compound interestCalculator

You invest 5,000 dollars at 4% annual interest, compounded monthly. How much is it worth after 6 years, to the nearest cent?

1. $6353.71$
2. $6200.00$
3. $6353.70$
4. $6326.60$

Question 7

Continuous growthCalculator

2,000 dollars is invested at 5% annual interest, compounded continuously. What is it worth after 10 years, to the nearest cent?

1. $3297.45$
2. $3000.00$
3. $3297.44$
4. $3257.79$

Question 8

Logarithmic equationsNo calculator

Solve $\ln x+\ln(x-3)=\ln 10$.

1. $x=5 \text{ or } x=-2$
2. $x=-2$
3. $x=10$
4. $x=5$

Question 9

Exponential modelsNo calculator

A substance decays from 80 grams to 20 grams in 12 years. What is its half-life, in years?

1. $6$
2. $3$
3. $4$
4. $24$

Question 10

Inverse functionsNo calculator

If $f(x)=3^x-2$, what is $f^{-1}(x)$?

1. $\log_{2}(x+3)$
2. $\log_{3}(x+2)$
3. $3^{x+2}$
4. $\log_{3}x+2$

Question 11

Domain of logarithmsNo calculator

For which values of $x$ is $f(x)=\log(2x-6)$ defined?

1. $x>-3$
2. $x>6$
3. $x>3$
4. $x\ge 3$

Question 12

Change of baseNo calculator

Evaluate $\log_8 4$.

1. $\frac{2}{3}$
2. $\frac{1}{2}$
3. $2$
4. $\frac{3}{2}$