## Unit 03 Business Mathematics (General Mathematics 9 PCTB)

Notes, solutions of unit 03, General Mathematics 9, for Punjab Curriculum & Textbook Board (PCTB), Lahore. * 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., $a^x = y \Longleftrightarrow log_ay = x, a > 0, a \neq 1 and y > 0)$.
- 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
- $log_a(mn) = log_am + log_an$,
- $loga (\frac{m}{n} ) = log_am – log_an$,
- $log_am^n = nlog_am$,
- $log_am log_mn = log_an$.

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

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