Product Rule: When multiplying like bases, add the exponents (
).Power Rule: The exponent on the argument can move to the front ( ).The Natural Log ( ): A special log with the base The Kingdom of Infinite Number: A Field Guide f...
): The exponent we were looking for.The Laws of the Land (Logarithm Rules): Product Rule: The log of a product is the sum of the logs ( Product Rule: When multiplying like bases, add the
).Quotient Rule: The log of a quotient is the difference of the logs ( This relationship is why we use logs to
).The Zero Power: Any base raised to the power of zero is always 1 (
Exponents and logarithms are two sides of the same coin. They undo each other. If you travel up a mountain using an exponent, the logarithm is the path back down to the base. This relationship is why we use logs to solve equations where the variable is trapped in the exponent. Applications in the Real World: