How to Evaluate Logarithms Without a Calculator

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on evaluating logarithms without the use of a calculator. It begins by establishing the fundamental relationship between logarithmic and exponential forms, teaching viewers to ask the question "Base raised to what power equals the argument?" The narrator progresses from simple integer examples to more complex scenarios involving common logarithms (base 10), negative exponents with decimals and fractions, and fractional exponents representing roots. The video systematically explores several key logarithmic properties, including the logarithm of 1, the logarithm of the base itself, and the inverse property where a base is raised to a logarithm of the same base. It places significant emphasis on mental math techniques, such as counting zeros to evaluate powers of 10 and understanding how reciprocal fractions relate to negative exponents. For educators, this resource serves as an excellent instructional tool for introducing or reinforcing the concept of logarithms in Algebra 2 or Pre-Calculus. The clear, step-by-step handwritten derivations on a blackboard style background make it easy for students to follow along. The video concludes with a mixed practice set, allowing teachers to pause and assess student mastery of various log evaluation techniques in a single session.