# Tutor profile: Jasmine H.

## Questions

### Subject: Pre-Calculus

Simplify the logarithmic function: 3 log (x) - 4log (x+3) + log (y)

Simplify each term: Step 1: Simplify 3 log (x) by moving 3 inside the logarithm and placing it as the (x) subscript log (x^3). Step 2: Simplify -4log (x+3) by moving 4 inside the logarithm and placing it as the (x+3) subscript. -log ((x+3)^4) After simplifying the first two terms we have: log (x^3) - log ((x+3)^4) + log (y) Step 3: Use the quotient property of logarithms, log (x) - log (y) = log (x/y). log (x^3/(x+3)^4) + log (y) Step 4: Use the product property of logarithms, log (x) + log (y) = log (xy). log (x^3/(x+3)^4) *y This can also be written as: log (x^3 * y/(x+3)^4) Apologies that I do not have a tool to make the exponents clearer. ^4=exponent

### Subject: Writing

In reading the question. Highlight the perceived error and make a recommendation for correction. Question: He gave his mother an extravagant gift after the argument. In spite of everything.

Answer: In spite of everything, he gave his mother an extravagant gift after the argument. Feedback: Subject-Verb Agreement Errors The subject and verb of a sentence must agree with one another in number whether they are singular or plural. If the subject of the sentence is singular, its verb must also be singular; and if the subject is plural, the verb must also be plural. Mistakes like these are often common when trying to structure a sentence the correct way. It is important to keep these tips in mind while writing and editing.

### Subject: Algebra

Simplify the following algebraic expression: 2(x - 9) + 6(-x + 2) + 4x

Step 1: Use the distributive property to multiply the term in front of each set of parenthesis. Note: Be careful of your signs and only multiply the number outside the parenthesis by every term inside the parenthesis. 2x-18+ -6x +2 + 4x Step 2: Organize and place all your like terms together in your expression. If the terms have an x attached to the number group them together. Group the numbers without a variable (x) together. Note: Do not forget your signs!! (be mindful, the 18 and the 6x in the expression is negative.) 2x - 6x + 4x + -18 + 2 Step 3: Combine like terms. All terms with the same variable should be combined (added/subtracted). All integers should be combined. (integers are negative and positive numbers.) 2x-6x+4x = 0x -18+2=-16 Step 3: Write the results of what is left as your final answer. There are two ways to express your final answer: a.) 0x - 16. or b.) -16 Both answers are equal.

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