UGA Trio UB/UBMS Algebra 6-23-2025
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Practice Problems on Evaluating Logarithms
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_2 2$
(b) $\log_5 1$
(c) $\log_{1/2} 2$ [/bluebox]
[solution] (a) $1$; (b) $0$; (c) $-1$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_3 3^7$
(b) $\log_4 64$
(c) $\log_{1/2} 0.25$ [/bluebox]
[solution] (a) $7$; (b) $3$; (c) $2$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_6 36$
(b) $\log_9 81$
(c) $\log_7 7^{10}$ [/bluebox]
[solution] (a) $2$; (b) $2$; (c) $10$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_2 32$
(b) $\log_5 5^{13}$
(c) $\log_6 1$ [/bluebox]
[solution] (a) $5$; (b) $13$; (c) $0$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_3 \left(\dfrac{1}{27}\right)$
(b) $\log_{1/3} 27$
(c) $\log_7 \sqrt{7}$ [/bluebox]
[solution] (a) $-3$; (b) $-3$; (c) $1/2$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Evaluate the following expressions:
(a) $\log_5 125$
(b) $\log_{49} 7$
(c) $\log_9 \sqrt{3}$ [/bluebox]
[solution] (a) $3$; (b) $1/2$; (c) $1/4$ [/solution]
Practice Problems on Logarithmic Equations
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_6 x = 2$
(b) $\log_{10} 0.001 = x$
[/bluebox]
[solution] (a) $36$; (b) $-3$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_{1/3} x = 0$
(b) $\log_4 1 = x$
[/bluebox]
[solution] (a) $1$; (b) $0$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_{4}\left(\dfrac{1}{64}\right) = x$
(b) $\log_{1/2} x = 3$
[/bluebox]
[solution] (a) $-3$; (b) $1/8$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_{9} \left(\dfrac{1}{3}\right) = x$
(b) $\log_{9} x = 0.5$
[/bluebox]
[solution] (a) $-1/2$; (b) $3$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_2\left(\dfrac{1}{2}\right) = x$
(b) $\log_{10} x = -3$ [/bluebox]
[solution] (a) $-1$; (b) $1/1000$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_x 1000 = 3$
(b) $\log_x 25 = 2$ [/bluebox]
[solution] (a) $10$; (b) $5$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Use the definition of the logarithm to find $x$:
(a) $\log_x 16 = 4$
(b) $\log_x 8 = \dfrac{3}{2}$ [/bluebox]
[solution] (a) $2$; (b) $4$ [/solution]
Project
A significant portion of your grade is built into completing a course project. If you work in a group, you will be required to submit peer evaluations as part of your progress reports. Late progress reports will have points deducted.
- Sign-up form: https://forms.gle/pugDSZCoMoqZ6AbR8
Timeline:
- Progress report (15% of project grade): Due June 27th.
- Progress report (15% of project grade): Due July 2nd.
- Project (70% of project grade): Due July 4th.
The following projects are available:
[bluebox] [bluetitle]Project 1 (Vieta’s Formulas).[/bluetitle]
Description: Students will make a poster or infographic that demonstrates how to use Vieta’s formulas to solve the following question: What two numbers add to $-1$ and multiply to $-1$?
This is a 3-4 student group project. [/bluebox]
[bluebox] [bluetitle]Project 2 (Logarithmic Scale Poster/Infographic).[/bluetitle]
Description: Students will research and make a poster or infographic showing real-life examples of logarithmic scales (e.g., Richter scale, decibel scale, pH scale, brightness of stars). The infographic must include an explanation of how logarithms apply.
This is a 3-4 student group project. [/bluebox]
[bluebox] [bluetitle]Project 3 (Exponential Growth and Money).[/bluetitle]
Description: Students will make a poster or infographic, using Desmos to model compound interest. Students will experiment with different parameters (principal, rate, compounding frequency) and show at least two graphs with a written interpretation of each graph.
This is a 3-4 student group project. [/bluebox]
[bluebox] [bluetitle]Project 4 (Solve Some Problems).[/bluetitle]
Description: Students will be given a few involved problems related to topics in the course, solve them, and produce a formal write-up detailing the solution. This can be done either individually or as a group project. [/bluebox]