In 3n, n is known as
=Base Constant Exponent
or Variable. please help me it's my exam
Answers
Answer:
Indices provide a compact algebraic notation for repeated multiplication. For example, is it much easier to write 35 than 3 × 3 × 3 × 3 × 3.
Once index notation is introduced the index laws arise naturally when simplifying numerical and algebraic expressions. Thus the simplificiation 25 × 23 = 28 quickly leads
to the rule am × an = am + n, for all positive integers m and n.
As often happens in mathematics, it is natural to ask questions such as:
Can we give meaning to the zero index?
Can we give meaning to a negative index?
Can we give meaning to a rational or fractional index?
These questions will be considered in this module.
In many applications of mathematics, we can express numbers as powers of some given base. We can reverse this question and ask, for example, ‘What power of 2 gives 16? Our attention is then turned to the index itself. This leads to the notion of a logarithm, which is simply another name for an index.
Logarithms are used in many places:
decibels, that are used to measure sound pressure, are defined using logarithms
the Richter scale, that is used to measure earthquake intensity, is defined using logarithms
the pH value in chemistry, that is used to define the level of acidity of a substance,
is also defined using the notion of a logarithm.
When two measured quantities appear to be related by an exponential function, the parameters of the function can be estimated using log plots. This is a very useful tool in experimental science.