Law of Logarithms

Law of Logarithms

Understanding Logarithmic Laws

• Multiplication Rule: The log of a multiplied by b is equal to the sum of the log of a and the log of b. This can be written as:
  • log(a * b) = log(a) + log(b)
• Division Rule : The log of a divided by b is equal to the log of a minus the log of b:
  • log(a / b) = log(a) - log(b)
• The power rule states the logarithm of a to the power of n equals n times the logarithm of a:
  • log(a^n) = n * log(a)

Change of Base Law

• Changing the base of the logarithm can be done using the change of base formula:
  • log_b(a) = log_c(a) / log_c(b)

Properties of Logarithms

• It’s essential to remember that a logarithm base b of a number x (written as log_b(x)) is the power to which the base b must be raised to get the number x.
• Logarithm of 1, regardless of the base, is always 0 because any number raised to the power of 0 equals 1.
• The base of a logarithm must be positive and cannot be 1, because 1 raised to any power is always 1 itself.

These rules help simplify complex logarithmic expressions and ease their computation. Having a clear understanding of them will provide smoother problem-solving.