6-Logaritmic-Functions.pptxdddddddddddddddddddddddddddddddddd

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1. LOGARITHMIC FUNCTIONS DOMINIC DALTON L. CALING General Mathematics | Grade 11

2. At the end of the lesson, you must be able to: define logarithmic functions; show illustrations of logarithmic functions that represent real-life situations; represent real-life situations using the logarithmic functions. LESSON OBJECTIVES

3. The inverse function is obtained by interchanging the roles of and . Thus, the inverse of the exponential function is . We can now say that in the equation , is the logarithm to which b must be raised to produce x. In the words, is the logarithm on b that produces . We write (read as “ equals the logarithm of to the base ”)   LOGARITHM

4. Let and be positive real numbers such that and . The logarithm of with base is denoted by , and is defined as if and only if .   LOGARITHM OF A NUMBER NOTE: Logarithmic functions and exponential functions are inverses. In logarithmic form , cannot be negative. The value of can be negative.  

5. 1. 2. 3. 4. 5.   EXAMPLES Exponential Form to Logarithmic Form

6. 1. 2. 3. 4.   EXAMPLES Logarithmic Form to Exponential Form

7. Common logarithms are logarithms with base 10, the base is usually omitted when writing common logarithms. This means that is written as and is written as and so on.   KINDS OF LOGARITHMS Natural logarithms are logarithms with base (which is approximately 2.71828 as mentioned in the previous module). This means that can be written as ln .  

8. EVALUATING LOGARITHMIC EXPRESSION

9. Find the value of each logarithm. 1. 2. 3. 4. 5.  

10. Some of the most common applications in real-life of logarithms are the Richter scale , sound intensity , and pH level . REAL-LIFE APPLICATIONS

11. Earthquake Magnitude on a Richter scale The magnitude R of an earthquake is given by: where E (in joules) is the energy released by the earthquake (the quantity is the energy released by a very small reference earthquake) The formula indicates that the magnitude of an earthquake is based on the logarithm of the ratio between the energy it releases, and the energy released by the reference earthquake.   RICHTER SCALE

12. In acoustics, the decibel (dB) level of a sound is where 𝐼 is the sound intensity in (the quantity is the least audible sound a human can hear).   SOUND INTENSITY

13. Acidic and basic are two extremes that describe a chemical property. Mixing acids and bases can cancel out or neutralize their extreme effects. A substance that is neither acidic nor basic is neutral. The pH scale measures how acidic or basic a substance is. The pH scale ranges from 0 to 14. A pH of 7 is neutral. A pH less than 7 is acidic. A pH greater than 7 is basic. The pH level of a water-based solution is defined as 𝑝𝐻 = −𝑙𝑜𝑔[𝐻+] where [𝐻+] is the concentration of hydrogen ions in moles per liter. pH SCALE

14. THANK YOU!