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Having previously defined what a logarithm is (see the notes on Functions and Graphs) we now look in more detail at the properties of these functions. The relationship between logarithms and exponentials is expressed as:
20 Μαρ 2020 · Download Matriculation Part-1 (Class IX) Maths Helping Notes of Chapter No 3 in high quality PDF Format only on Taleem360.
• Solve logarithmic equations using the properties of logarithms. Common Logarithms(pp. 547–553) 1 1 0.5 0.5 • Solve exponential equations and inequalities using common logarithms. • Evaluate logarithmic expressions using the Change of Base Formula. Follow-Up: Solving Exponential and Logarithmic Equations and Inequalities
Exponential functions have many applications and play a big role in this course. Working with them requires understanding the basic laws of exponents. This chapter reviews these laws before recalling exponential functions. Then it explores inverses of exponential functions, which are called logarithms.
The formula y = logb x is said to be written in logarithmic form and x = by is said to be written in exponential form. In working with these problems it is most important to remember that
solve simple equations requiring the use of logarithms. Why do we study logarithms ? What is a logarithm ? 4. Exercises. 5. The first law of logarithms. 6. The second law of logarithms. 7. The third law of logarithms. 8. 9. 10. 11. 12. 13. 14. 1. Introduction. In this unit we are going to be looking at logarithms.
1 EXPONENTS AND LOGARITHMS WHAT YOU NEED TO KNOW • The rules of exponents: • ma m× an = a +n • a a a m n = mn • (am)n mn= a • aa m n n m • a a n n − = 1 • an × nb = (ab)n • a b a b n n n = ⎛ ⎝⎜ ⎛ ⎝ ⎞ ⎠⎟ ⎞ ⎠ • The relationship between exponents and logarithms: • ab=⇔b xb g a where a is called the ...
