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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 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 ...
If a denotes any positive real number and “b” any real number except 1, then there is a unique real number, called the logarithm of a with base “b” (logb a), which is the exponent in the power of “b” that equals a; that is,
Logarithms were originally developed to simplify complex arithmetic calculations. They were designed to transform multiplicative processes into additive ones.
What does it mean? First of all the assumptions (restrictions) are important. The number a, called the base of the logarithm, has to be greater than 0 and cannot be equal to 1. The number b (which we take the logarithm of) has to be greater than 0. So the expressions like log1 3, log 2 5 numbers (similarly to expressions like. p or log4( 6).
Essential Question. What are some of the characteristics of the graph of a logarithmic function? Every exponential function of the form f (x) bx, where b is a positive real number. = 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.
a function that can be used to answer the question ‘what is the number which when put as the exponent of 10 gives this value?’ Th is function is called a base-10 logarithm, written log 10. In the above example, we can write the solution as x = lo g 10 50 . More generally, the equation y =10 x can be re-expressed as xylog . In fact, the base ...
Simplify each of the following logarithmic expressions, giving the final answer as a number not involving a logarithm. a) log 4 log 0.52 2− b) log 10 log 52 2− c) 2log 4 log 82 2+ d) 2log 5 2log 0.2520 20− e) 3log 8 3log 324 24+ 3 , 1 , 7 , 2 , 3
