### Laws of Logarithms

a) log y = 1.2x -1 b) ln y = 1.2x - 1

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

- Mathematics
- /
- Algebra
- /

a) log y = 1.2x -1 b) ln y = 1.2x - 1

See the attached file. 1. Solve the radical equation: {see attachment} 2. Find the equation of the line through the point (-2,-4) and perpendicular to the line {see attachment} 3. Complete the square, find the vertex, the axis of symmetry, all the intercepts, and graph the parabola: {see attachment} 4. ... Find the

Please tell me whether or not the 2 correspondences are upper hemicontinuous and PLEASE (using the definition) justify why. 1)F:[2,3]->R^2, F(r)={(x,y):abs(x)+abs(y)<=r} 2)F:R^n{0}->R^n, F(x)=B(x;||x||), the closed ball centred at x with radius ||x||. Thanks Note: abs=absolute value is the complement ||x|| is d

Section on using the properties of algebraic, trigonometric, logarithmic and exponential functions to solve problems. 1) Solve the following equation: log5 X + log5(X-2) = log5 X 2) The half-life of a certain radioactive element is 100days. That means that after 100 days ½ of the radioactive substance wil

Consider the following grid: 1) How many squares (of all sizes) are there in this grid? 2) How many rectangles (of all sizes) are there in this grid? 3) Can you generalize your results to an n by n grid? Can you generalize further? Please see attachment for grid.

Classify the 15 given polynomials as monomials, binomials, trinomials, and polynomials. Use the format given below for categorizing the polynomials. [Note: Simplify wherever possible] (Please see attachment for polynomials)

1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1. 2. You are given the following polynomial: 2x7 - 4x3 + 3x. If x were replaced with its opposite in each of the terms of the given polynomial, will it result in the opposite of the polynomial? Explain why or why not and illustrate to supp

a) Write an expression in sigma notation as shown for suitable terms n1, n2, and ai, for each of these finite and infinite summations. b) Use the method of telescopic sums to evaluate these finite sums, using the indicated anti-difference sequences. c) Which of the following sequences are null? Explain your answer. See

The sum of 2 nonnegative numbers is 20. Find the numbers if: a)if the product of one number and the square root of the other is to be as large as possible, and b)if one number plus the square root of the other is to be as large as possible.

Number Theory - Polynomial Congruences Find all solutions of each of the following congruences . (a) x2 + x +1 ≡ 0 (mod 11)

# Recall that a binary tree can be defined recursively as: * A Binary Tree is either empty * or A Binary Tree consists of a node with a left and right child both of which are Binary Trees. The degree of a node in a tree is equal to 0 if both children are empty, 1 if one of the children are empty, and 2 of both children ar

Consider the grammar 1) <Number> -> <Digit><Number>|epsilon 2) <Digit> -> 0|1|2|3|4|5|6|7|8|9 Use induction to show that the number of strings in L(<Number>) of length n is equal to 10^n

3. Lisa is coloring her creation. The blue color used is 50% of the green color used, yellow is 5% of the blue color used, and brown is 7% of the amount of green used. She wants to find the total amount of color used by her. a. Find the total amount of color used by Lisa using an algebraic expression. b. Comment on the kind of

2. Mr. Pinto is a Web designer. He is trying to put 4 characters on a page. The space occupied by character 2 takes 5 units more than character 1, character 3 takes 7 units less than the character 2, and character 4 takes the same space as that taken by character 2. a. Find the total space occupied by all the characters in an a

1. Three prizes are to be distributed in a Creative Design Talent Search Contest. The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize. a. Express the total value of the three prizes as an algebraic expression. b. Comment on the ki

See the attached file. Solve each compound inequality and write the solution set using interval notation. 80) 0< 5-2x <=10 -6< 4-x<0 81) -3 < (3x -1)/ 5 < ½ 1/3 < (3-2x)/6 < 9/2 86) Selling Price Range: Renee wants to sell her car through a broker who charges a commission of 10% of the selling price. The book val

Translate the following into algebraic expressions. Clearly identify the variables, coefficients, and constants: a) One fourth of one half of the product of two numbers b) Two-thirds of the quotient of two numbers c) The product of 7 and twice n

Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. Form an algebraic equation to express this and identify the variables, coefficients, and constants of the algebraic expression. You are not required to solve the equation.

1. In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle. [The sum of the measures of three interior angles of a triangle is always 180 degrees.] Form an algebraic equation to express the problem and identify the variables, coefficients,

The stability number, alpha(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that no two of the vertices in S are connected by an edge of G. The clique number, omega(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that every pair of

Write productions that will define the syntactic category <SimpleStat>, to replace the abstract terminal simpleStat in the figure below {see attachment}. You may assume the syntactic category <Expression> stands for C arithmetic expressions. Recall that a "simple statement" can be an assignment, function call, or jump, and that

Please remember to show your methodology as well as the answer. How you solved the problems remember to follow logical rules AND PLEASE BE CAREFUL - CHECK YOUR ARITHMETIC WATCH OUT FOR THOSE QUESTIONS THAT NEED ± SOLUTIONS There are 25 questions. For questions 1 through 9, perform the indicated operations. If possib

Let S = Z_43 (where the underscore, "_", indicates that what follows it, in this case 43, is a subscript). Let Q be a subset of S that contains ten non-zero numbers (i.e., that Q contains ten non-zero elements of S). Prove that Q contains four distinct numbers "a," "b," "c," "d" such that ab = cd in Z_43.

Five children collect N pieces of Halloween candy and decide to split it evenly among them. When they try to divide it they have two pieces of candy left over. One of the children leaves, taking the 26 pieces of candy she collected with her. The remaining four children try to split the N-26 remaining pieces of candy and discover

1. For the quadratic equation y = cx² + dx + e (where c, d and e are constants), what is the x-coordinate of the vertex? 2. For the same quadratic equation as above, what is the y-intercept? 3. Solve by the square root property: 4x² = 100 4. Solve by completing the square: x² - 10x + 4 = 0 5. Solve by usin

Please see the attached file for the fully formatted problems. Q1. Solve {see attachment} Q2. Solve 9 - 7+15/5 - (6-3)4 Q3. Solve {see attachment} Q4. Find the equation for the line with slope 3/5 and passing through the point (4, 2). Q5. Solve |2x-5| >= 14 Q6. A store issued coupons worth 20% off from any pu

1. The width of a rectangle is 8 feet less than the length. If the area is 20 square feet, find the length and the width. 2. Solve the equation: x(x - 4) = 12 3. A boat travels 30 miles upstream against the current in the same amount of time it takes to travel 42 miles downstream with the current. If the rate

INSTRUCTIONS TO OTA 1. typeset solutions 2. send solution as attachment 3. Use words to explain solutions. DO NOT RELY ONLY ON ALGEBRAIC MANIPULATIONS/ OR SYMBOLS. Find the smallest positive integer N such that N/2 is a perfect square, N/3 is a perfect cube and N/5 is a perfect fifth power.

Let a and b be integers. A common multiple of a and b is an integer n for which a|n and b|n. We call an integer m the least common multiple of n provided (1) m is positive, (2) m is a common multiple of a and b, and (3) if n is any other positive common multiple of a and b, then n [greater than or equal to] m. The notation fo

See attached file...it is a full induction proof of Cauchy Integral Formula, with the base case step missing. All I have to do is show that it holds for "n=1", using the rest of the proof as an example...however i am having trouble showing it.