Exponents and Logarithms

WEEK 3

Unit 3:Exponents and Logarithms

Students Learning Outcomes: After studying this unit, the students will be able to:

• express a number in standard form of scientific notation and vice versa.

• define logarithm of a number y to the base a as the power to which a must be raised to give the number (i.e., ax = y ⇔ loga y = x, a > 0, • a ≠ 1 and y > 0).

• define a common logarithm, characteristic and mantissa of log of a number.

• use tables to find the log of a number. • give concept of antilog and use tables to find the antilog of a number.

• differentiate between common and natural logarithm.

• prove the following laws of logarithm

• loga (mn) = loga m + loga n,

• loga ( ) = loga m – loga n,

• loga mn = nloga m,

• loga m logmn = loga n.

• apply laws of logarithm to convert lengthy processes of multiplication, division and exponentiation into easier processes of addition and subtraction etc.

 Introduction to Logarithms

Logarithm Logarithms areusefultools for accurate andrapidcomputations. Logarithms with base 10 are known as common logarithms and those with base e are known as natural logarithms. We shall define logarithms with base a > 0 and a ≠ 1.

For detailed explanation consult PTB 9th Science Mathematics Book Unit # 03 Logarithm, Page 31

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