Nicole S.

Math Major at University of California, Davis

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Pre-Calculus

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Question:

Solve the equation 3(5^{2x+1})=18(2^{5x-3}), and write your answer using natural logarithms.

Nicole S.

Answer:

Dividing both sides of 3(5^{2x+1})=18(2^{5x-3})$by 3 gives 5^{2x+1}=6(2^{5x-3}), and then taking natural logarithms of both sides gives (2x+1)\ln 5=\ln 6+(5x-3)\ln 2. Then 2x\ln 5+\ln 5=\ln 6+5x\ln 2 -3\ln 2, so (2\ln 5)x-(5\ln 2)x=\ln 6-3\ln 2-\ln5 and therefore (2\ln 5-5\ln 2)x=\ln 6-3\ln 2-\ln5.

Trigonometry

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Question:

Find the point on the Unit Circle associated with the angle 5π/3

Nicole S.

Answer:

(1 / 2 , -√3 / 2)

Algebra

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Question:

Evaluate: 30 - 12÷3×2 =

Nicole S.

Answer:

22

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