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to logarithms. In the lessons to follow we will learn some important properties of logarithms. One of these properties will give us a very important tool which we need to solve exponential equations. Until then let’s practice with the basic themes of this lesson.
•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 ...
In this unit you will examine the definition and inverse relationship with the exponential function, practice the laws of logarithms, solve logarithmic equations, and explore a more efficient method for solving equations using the “Change of Base” formula for logarithms.
We use can logarithms to solve exponential equations: The solution of ax = b is x = log a b For example, the solution of ex = 2 is x = log e 2. To find the value of this logarithm, we need to use a calculator: log e 2 = 0.6931. Note Logarithms were invented and used for solving exponential equations by the Scottish baron John Napier (1550 ...
Defining Logarithmic Functions – The function yx logb is the name we give the inverse of yb x. For example, yx log2 is the inverse of 2 y x. Based on Exercise #1(d), we can write an equivalent exponential equation for each logarithm as follows: log is the same as y yx bx b
• All logs must be to the same base in applying the rules and solving for values • The most common base for logarithms are logs to the base 10, or logs to the base e (e = 2.718281…) • Logs to the base e are called Natural Logarithms logex = ln x If y = exp(x) = ex Then loge y = x or ln y = x
What are some of the characteristics of the graph of a logarithmic function? other than 1, has an inverse function that you can denote by g(x) = logb x. This inverse function is called a logarithmic function with base b. Work with a partner. Find the value of x in each exponential equation. Explain your reasoning.
