Frequently Asked Questions.
Find quick, intuitive answers to common questions about logarithms, laws, properties, and resources.
Where can I download the Logarithm Formula Sheet PDF?
You can download the Logarithm Formula Sheet PDF directly from the Logarithm Formulas & Properties Sheet! Just click the highlighted Print / Save PDF button at the top of that page, and select "Save as PDF" as your destination in your print dialog. This generates a clean, single-page reference sheet.
What is a logarithm in simple terms?
A logarithm answers the question: "How many of one number do we multiply together to get another number?" For example, to get 8 from multiplying 2s, we need 3 of them (2 × 2 × 2 = 8). So, the logarithm of 8 with base 2 is 3, written as log2(8) = 3.
What are the 3 main laws of logarithms?
The three primary laws of logarithms are:
1. Product Rule: logb(x • y) = logb(x) + logb(y)
2. Quotient Rule: logb(x / y) = logb(x) - logb(y)
3. Power Rule: logb(xk) = k • logb(x)
Why do we add logarithms when multiplying?
Because logarithms represent exponents (powers). When you multiply numbers with the same base (such as 102 × 103), you add their exponents together (102+3 = 105). Since logs calculate exponents, multiplying inside a logarithm corresponds to addition outside.
Are logarithm cheat sheets free to download?
Yes! The logarithm formula sheet and print-friendly reference card on this website is 100% free to print or save as a PDF. No registration, signup, or email is required.
Can I use this log properties guide for high school and college math?
Absolutely. This guide and PDF sheet covers basic algebraic rules (product, quotient, power rules), base changes, natural logarithms (ln), and calculus derivatives of logarithmic functions.
How do you undo a natural logarithm?
You undo a natural logarithm (ln(x)) by applying its inverse function, which is the natural exponential function (ey). For example, if ln(x) = y, then x = ey.