In previous lessons, we have covered a few different problems concerning exponents. Today's lesson turns the idea of exponents on its head. This concept appeared 22 times last year, with a median placement at question # 63.
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Number Dojo Level: 295
The logarithm of a number is the exponent to which another number, the base, must be raised to produce that number. So in logarithmic notation,
There are several important formulas concerning logarithms that need to be learned:
- Product: The logarithm of a product is the sum of the logarithms of the numbers being multiplied.
- Quotient: The logarithm of the ratio of two numbers is the difference of the logarithms.
- Power: The logarithm of the p-th power of a number is p times the logarithm of the number itself.
- Root: The logarithm of a p-th root is the logarithm of the number divided by p.
Change of Base
There is one other formula that will be useful concerning logarithms.