Evaluating logarithms using change-of-base formula

What You'll Learn

Apply the change-of-base formula to rewrite logarithms with any base

Convert logarithmic expressions into calculator-ready form using common logarithms

Evaluate logarithms with non-standard bases using a scientific calculator

Solve logarithmic equations by combining change-of-base with exponential form conversion

What You'll Practice

Rewriting logarithms in multiple equivalent forms using different bases

Calculating decimal values of logarithms with bases other than 10

Evaluating expressions with coefficients and complex arguments like fractions and radicals

Solving equations where the variable appears in the base or argument of a logarithm

Why This Matters

The change-of-base formula unlocks your calculator's full potential for logarithmic work. Since most calculators only have log base 10 and ln buttons, this formula lets you evaluate any logarithm you encounter in advanced algebra, calculus, and science courses.

Before You Start — Make Sure You Can:

Converting from logarithmic form to exponential form Evaluating logarithms without a calculator Common logarithms

This Unit Includes

7 Video lessons

Practice exercises

Skills

Change-of-Base Formula

Logarithms

Calculator Skills

Exponential Form

Equation Solving

Algebraic Manipulation

OH Curriculum Aligned