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•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 law of logarithms log a xm = mlog a x 5 7. The third law of logarithms log a x y ...
How do we decide what is the correct way to solve a logarithmic problem? The key is to look at the problem and decide if the problem contains only logarithms or if the problem has terms without logarithms.
In this booklet we will demonstrate how logarithmic functions can be used to linearise certain functions, discuss the calculus of the exponential and logarithmic functions and give some useful applications of them.
Sample Exponential and Logarithm Problems 1 Exponential Problems Example 1.1 Solve 1 6 3x 2 = 36x+1. Solution: Note that 1 6 = 6 1 and 36 = 62. Therefore the equation can be written (6 1) 3x 2 = (62)x+1 Using the power of a power property of exponential functions, we can multiply the exponents: 63x+2 = 62x+2 But we know the exponential function ...
Since the scatter plot does not appear to flatten out as much as a decaying exponential function would, we will look for a logarithmic model of the form y = a + b ln x where b < 0 for the data. y = a + b ln x, use LnReg from the STAT CALC screen. y = 34.1786 - 5.6826 ln x.
A logarithm is just an index. We use log as an abbreviation for the word logarithm. To find the value of a logarithm we need to solve an exponential equation. Example (a) The solution of 2x = 8 is x = 3. We can write this in logarithm notation as log 2 8 = 3 ‘log of 8 to base 2 is 3’ (b) x = 5 is the solution of 2x = 32.
To solve equations which involve logarithms or exponentials we need to be aware of the basic laws which govern both of these mathematical concepts. We illustrate by considering some examples.
