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Samantha W.
Civil Engineering major at Duke University (Class of '21)
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Pre-Calculus
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Question:

How do I add & subtract logarithms?

Samantha W.

To add or subtract logarithms, you first need to ensure that the logarithms you are adding/subtracting have the same "base" number. This is the number that is a subscript in logarithm notation - for example, log$_{10}$(2) has a base number of 10. To change the base of a logarithm from $a$ to $b$, you can use the Change-of-Base formula, which is as follows: log$_{a}(x)$ = log$_{b}(x)$ / log$_{b}(a)$. To add logarithms with the same base, you multiply the content inside the parentheses. For example, log$_{b}(x)$ + log$_{b}(y)$ = log$_{b}(xy)$. To subtract one logarithm from another logarithm with the same base, you divide the content inside the positive logarithm's parentheses by the content inside the negative logarithm's parentheses. For example, log$_{b}(p)$ + log$_{b}(q)$ = log$_{b}(\frac{p}{y})$.

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Question:

I volunteered building latrines in Costa Rica during a week-long mission trip, and it was really transformative. Should I write my college essay about this experience?

Samantha W.

While your experience may have been meaningful, writing about your mission trip experience runs the risk of conveying a lack of creativity. Thousands of students have written college essays about how they too were transformed by exposure to Third World Poverty on a mission trip, making it one of the most popular, yet unoriginal and clichéd college essay topics. If you would still like to write about this experience, I would advise you to avoid repeating this trope in favor of (1) demonstrating sustained involvement in volunteer service, (2) demonstrating the tangible, long-term influence of this trip on your life, (i.e. action that you took as a result of the experience), or (3) approaching the mission trip topic from an original perspective. For example, I wrote my experience volunteering in the Dominican Republic as part of a series of experiences that transformed me from a shy, relatively insecure girl to a confident, assertive woman with intent to pursue a career in international development. I demonstrated sustained passion for international development by writing about a fundraising effort I led for the non-profit with which we partnered and a high-school club I founded as a result of this experience. Another way to approach this topic might be to write about an ethical dilemma you encountered as a result of this experience. Nevertheless, there still exists a significant risk of repeating clichés, so I would advise you to avoid writing about your mission trip experience unless you are certain that your essay will stand out from the thousands of mission-trip essays submitted every year.

Algebra
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Question:

What is the slope of the graph created by 3y + 4x = 27?

Samantha W.

The slope of this graph is -4/3. 1/3*(3y + 4x) = 1/3*(27) (y + 4/3x) - 4/3x = (9) - 4/3x y = -4/3x + 9 y = mx + b, where m is the slope. --> slope = -4/3x

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