Again, this can alternatively be expressed as Will use them interchangeably in this work.įor example. Iii) The power can either be same or different.Ģ They are also referred to as theorems, laws and properties. Ii) The sign between the terms must be a multiplication and not I) The terms must have the same base otherwise the law cannot beĮxample because 5 and 6 are not like base. The following should be noted about this rule: Operations and they will be discussed in this section.įor example. Useful and compact way to express numbers. Undoubtedly one would need to carry out calculations in index Like any integer can be written in the formĮxpressed in both index and fractional forms as and The next question that might come to mind is whether any number Is a better way of writing a cumbersome 1 000 000 000.Ĭan be carried out on a scientific calculator, commonly via aġ Precisely, we mean indicial and logarithmic functions. Need indices to express numbers such as in the example not onlyĪnd time but more importantly it is sometimes easy to remember Now let us work in the reverse order and findĬan be written as a multiple of tens, i.e.Īnd it is the same as (a billion).
So what do you think about ? It is in value but it is written Read as five to the power three or five cubed. What does this imply? Itīeen multiplied by itself times. Is the most frequently used as such, is read as raised to the Of the terms (index, exponent or power) is used more than the , could also be referred to as aĪll essentially mean the same. Well, indices is when a number is expressed in the form where isĪnd the index. Readers are reminded that this part of theīackground regarding the topic and therefore few examples willĬomprehensive and varied examples, do refer to the Worked Graphs of their functions will not be covered here as these will
#Condense logarithms .pdf how to#
How to solve their equations using certain rules that will be
Here we will take a look at how to simplify exponential and In fact they are part of ourįinance, economics and natural phenomenon, although we use them Most of the equations we encounter,Ĭomplex forms, are based on them. index) together with logarithms1 are central toĮngineering processes. SECTION 15: SOLVING COMMON LOGARITHMS USING LOG-ANTILOG TABLES SECTION 12: INDICIAL EQUATIONS (III) (INVOLVING LOGARITHMS) SECTION 11: INDICIAL EQUATIONS (II) (UNKNOWN AS THE INDEX) SECTION 10: INDICIAL EQUATIONS (I) (UNKNOWN AS THE BASE) SECTION 9: CONVERSIONS BETWEEN INDICES AND LOGARITHMS (ADVANCED) SECTION 8: FINDING ANTI-LOGARITHMS OF NUMBERS SECTION 6: APPLICATIONS OF LAWS OF LOGARITHMS SECTION 5: CONVERSIONS BETWEEN INDICES AND LOGARITHMS (BASIC) SECTION 4: APPLICATIONS OF LAWS OF INDICES (SIMPLIFICATION) SECTION 3: ADVANCED APPLICATIONS OF LAWS OF INDICES SECTION 2: BASIC APPLICATIONS OF LAWS OF INDICES (NUMBERS AND SECTION 1: BASIC APPLICATIONS OF LAWS OF INDICES (NUMBERS ONLY) Or omissions, either accidently or otherwise in the course of The author does notĭisclaims any liability to any party for any loss, damage, or The author has exerted all effort to ensure an accurate Pertinent suggestions, feedbacks and queries are highly welcome Malaysia), Teslim Abdul-Kareem (formerly with University ofĪbdul-Aziz Apalara (KFUPM, Saudi Arabia), Jimoh JR Ibrahim Advanced learners, particularly thoseīreak from the academic environment, will also find thisīe used as a reference guide by teachers, tutors, and otherĪnd for assessment (home works and examinations).įinally, many thanks to my colleagues who have offeredĮspecially Khadijah Olaniyan (Loughborough University, UK), Dr.īalogun (Universiti Teknologi PETRONAS, Malaysia), Sakiru Those in mathematics and engineering textbooks designed for There are two main parts in this book one gives a broad Worked examples complemented with a comprehensive background on Your hands is another book for potential mathematicians,Ĭurrent work Indices and Logarithm Explained with Worked After a successful dissemination of the previous books, which
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