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# Tutor profile: Samantha W.

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Samantha W.
Civil Engineering major at Duke University (Class of '21)
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## Questions

### Subject:Pre-Calculus

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Question:

How do I add & subtract logarithms?

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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?

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Samantha W.

### Subject:Algebra

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Question:

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

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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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