Problem Set 1

1. Solve for $x$ in each of the expressions by hand. Show all of your work.

$$8x-1=6$$

$$x^2+13x+1=10$$

$$\frac{x^2+8x+15}{x+5}=0$$

$$lo{g}_2(4x)=6$$

$$2^x=13$$

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2. Solve for $x$ in each of the expressions using any calculators or tools at your disposal (e.g. Desmos, Wolfram, etc.). Write a sentence or two on the strategy you used to solve each problem.

$$lo{g}_3(5x)+x=7$$

$$\frac{x-5}{lo{g}_2(x-4)+1}=35$$

$$2^x-x^2=10$$

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3. Write pseudocode for a function that finds the smallest number in a non-empty, unsorted array of integers.

Hint!

What kind of search algorithm can be used on an unsorted list of data?

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4. Write pseudocode for a function that takes an integer as an argument and returns true if it is a power of two and false otherwise.