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explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms. Contents. Introduction. Why do we study logarithms ? What is a logarithm ? if x = an then loga x = n. 4. Exercises. 5. The first law of logarithms. loga xy = loga x + loga y. 6. The second law of logarithms.
Objectives: 1) Use properties of logarithms to evaluate, condense, and solve equations using natural logs. The history of mathematics is marked by the discovery of special numbers such as counting numbers, zero, negative numbers, , and imaginary numbers.
Introduction to Logarithms. In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. So the logarithm is 3. How to Write it. We write it like this: log2(8) = 3.
Logarithms are very useful mathematical entities that have an enormous amount of application to real-world situations. Combined with their inverse relationship to the exponential functions, logarithms allow for the simplification of complex problem situations to basic arithmetic operations.
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:
1.2 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
26 Μαρ 2016 · Logarithms are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions (logs), remember this inverse relationship and you'll be solving logs in no time!
