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This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
In this lesson we will further explore graphs of these logarithms, including their construction, transformations, and domains and ranges. Exercise #1: Consider the logarithmic function yx log 3 and its inverse y 3 x .
•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
Use logarithmic functions to model and solve real-life problems. Every function of the form f (x) = ax passes the Horizontal Line Test and therefore must have an inverse function. This inverse function is called the logarithmic function with base a. are equivalent.
Exponential functions and logarithm functions are important in both theory and practice. In this unit we look at the graphs of exponential and logarithm functions, and see how they are related.
pH of solution = −n = − log [ H+]. The negative sign is used to avoid always having negative pH’s, since the concentration [ H+] is very small. The algebraic laws. We will begin with a brief review of the algebra of exponentials and logarithms. Please study the examples given of calculations, since many students seem to have trouble with this.
Logarithms which are not whole numbers are the logs of numbers which cannot be written as 1 and a string of zeros. For example the log of 2 is 0.30103 and the log of 5 is 0.69897. Of course, these add to 1, the log of 10, because 2 × 5 = 10: 0.30103 + 0.69897= 1.0000 Negative logarithms are the logs of numbers less than one. For example, the ...
