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.