Properties of logarithms Study guides, Class notes & Summaries
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update 
properties of exponents 
- whole number exponents: b^n = b • b • b... (n times) 
- zero exponent: b^0 = 1; b ≠ 0 
- negative exponents: b^-n = 1/(b^n); b ≠ 0 
- rational exponents (nth root): ^n√(b) = 1/(b^n); n ≠ 0, and if n is even, then b ≥ 0 
- rational exponents: ^n√(b^m) = ^n√(b)^m = (b^(1/n))^m = b^(m/n); n ≠ 0, and if n is even, then b ≥ 0 
 
 
operations with exponents 
- multiplying li...
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS LATEST VERSION] UPDATED | 2024
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS LATEST VERSION] UPDATED | 2024 
 
 
 
 
 
 
properties of exponents	- whole number exponents: b^n = b • b • b... (n times) 
- zero exponent: b^0 = 1; b ≠ 0 
- negative exponents: b^-n = 1/(b^n); b ≠ 0 
- rational exponents (nth root): ^n√(b) = 1/(b^n); n ≠ 0, and if n is even, then b ≥ 0 
- rational exponents: ^n√(b^m) = ^n√(b)^m = (b^(1/n))^m = b^(m/n); n ≠ 0, and if n is even, then b ≥ 0 
operations with exponents	- multi...
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College Algebra CLEP Exam questions and answers 100% correct
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College Algebra CLEP Exam questions and answers 100% correct 
The Quadratic Formula 
 
 
 
Same base, different exponents 
add exponents 
 
 
 
Different base, same exponent 
multiply bases together 
 
 
 
y=logₙ(x) --> 
x=n^y 
 
 
 
Properties of Logarithms 
logₙ(xy) = ? 
logₙ(x) + logₙ(y) 
 
 
 
Properties of Logarithms 
logₙ(x/y) = ? 
logₙ(x) - logₙ(y) 
 
 
 
Properties of Logarithms 
logₙ(x^y) = ? 
ylogₙ(x) 
 
 
 
Properties of Logarithms 
logₙ(1) = ? 
0 
 
 
 
logₙ(...
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MATH 115 QUIZ 3 / QUESTIONS AND CORRECT ANSWERS 2023/2024.
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MATH 115 QUIZ 3 / 
QUESTIONS AND 
CORRECT ANSWERS 
2023/2024. 
SOLUTONS 
1. 
 (a) Let x=log6 
1 
7776 State the corresponding exponential form of this logarithmic equation. 
logb 
v=x 
means 
v=b 
x 
Thus, the exponential firm of this equation is 
6 
x= 
1 
7776 
 (b) Determine the numerical value of log6 
1 
7776 in simplest form. 
Note that 7776=6 
5 
. Thus 
1 
7776 
=6 
−5 
So, we have 
6 
x=6 
−5 
x=−5 
2. Use an appropriate change of base formula to approximate log3 36 to the nearest...
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ALEKS CALCULUS PREP WITH COMPLETE SOLUTIONS 100% 2023/2024
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ALEKS CALCULUS PREP WITH COMPLETE SOLUTIONS 100% 2023/2024 
What is the equation for finding the length of an arc based on radians or degrees? 
length = radius * RADIANS 
 
 
How to convert radians to degrees 
multiply the radians by (180/pi) 
 
 
What is the law of cosines 
 
 
What is the law of sines 
 
 
How to determine the terminal point for a radian (ex. 2*pi) 
The terminal point is the coordinate on the graph. It is usually a combination of 1, 0, and the square root of 2 over 2 
 
 
What...
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ALEKS CALCULUS PREP WITH COMPLETE SOLUTIONS 100% 2023/2024
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ALEKS CALCULUS PREP WITH COMPLETE SOLUTIONS 100% 2023/2024 
What is the equation for finding the length of an arc based on radians or degrees? 
length = radius * RADIANS 
 
 
How to convert radians to degrees 
multiply the radians by (180/pi) 
 
 
What is the law of cosines 
 
 
What is the law of sines 
 
 
How to determine the terminal point for a radian (ex. 2*pi) 
The terminal point is the coordinate on the graph. It is usually a combination of 1, 0, and the square root of 2 over 2 
 
 
What...
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College Algebra CLEP Exam
- Exam (elaborations) • 4 pages • 2023
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Same base, different exponents - Answer-add exponents 
Different base, same exponent - Answer-multiply bases together 
y=logₙ (x) --> - Answer-x=n^y 
Properties of Logarithms 
logₙ (xy) = ? - Answer-logₙ (x) + logₙ (y) 
Properties of Logarithms 
logₙ (x/y) = ? - Answer-logₙ (x) - logₙ (y) 
Properties of Logarithms 
logₙ (x^y) = ? - Answer-ylogₙ (x) 
Properties of Logarithms 
logₙ (1) = ? - Answer-0 
logₙ (a^x)= - Answer-x 
a^logₙ (x)= - Answer-x 
If the answer to an ab...
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OnRamps- FURTHER ALGEBRA – A BRIDGE TO ABSTRACTION A COLLEGE ALGEBRA COURSE CONTAINING ALGEBRA II 2021-2022. Entire Text. PlusQuestions and Worked Solutions.
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OnRamps- FURTHER ALGEBRA – A BRIDGE TO ABSTRACTION A COLLEGE ALGEBRA COURSE CONTAINING ALGEBRA II 2021-2022. Entire Text. PlusQuestions and Worked Solutions. 1 Essential Prerequisites 1 1.1 Prerequ isites . 1 1.2 Thinking Like a Mathematician . . 7 1.3 Prerequisite Topics Review . . 7 2 Functions 13 2.1 Functions 13 2.2 Linear and Absolute Value Functions . 18 2.3 Composition of Functions . . 28 2.4 A Function Recursive Process 30 2.5 Function Transformations . . 31 2.6 Inverse of a Function ....
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Act Math Test Practice 40 Questions with Verified Answers,100% CORRECT
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Act Math Test Practice 40 Questions with Verified Answers 
 
Integrating Essential Skills, Ratios, Proportions, and Percent 
 
On a map, 1/2 inch represents 16 miles. How Many miles long is a road that is 4-3/4 inches on the map? 
A 
76 
B 
112 
C 
128 
D 
139 
E 
152 - CORRECT ANSWER 0.5/16 = 4.75/x (Cross Multiply to find X) -----> x = 152 Miles (E) 
 
Integrating Essential Skills, Ratios, Proportions, and Percent 
 
If -4 ≤ x < 2 and x is an integer, how many different values can x ha...
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CS 3303 Data Structures Study Guide | 100 Questions with 100% Correct Answers | Verified | Latest Update 2024
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A solution is said to be efficient if it: - Solves the problem within the required resource constraints 
An ADT is: - The realization of a data type as a software component 
The implementation of a data type as a data structure is the physical form of an ADT. - True 
Which of the following is NOT one of the design patterns outlined in our text. - Synergy 
If A={1, 2, 3, 4} and B={4, 5, 6}, find A∪ B . - {1,2,3,4,5,6} 
According to the properties of logarithms, log(nm) = 
Note: Due to issues wi...
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