TOPIC
MY PROGRESS
Pug Score
0%
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Get Started
Get unlimited access to all videos, practice problems, and study tools.
Unlimited practice
Full videos
Back to Menu
Topic Progress
Pug Score
0%
Videos Watched
0/0
Best Practice
No score
Read
Not viewed
Best Quiz
No attempts
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Overview
Integrated Mathematics III
16. CC.HSF.BF.B.5
16.8 Evaluating logarithms using change-of-base formula
Change of Base Formula for Logarithms
Learn how the change of base formula lets you evaluate any logarithm with a calculator, including its proof and worked examples.
What You'll Learn
The change of base formula rewrites log base b of x as a fraction of two logarithms in a base you can actually compute.
Most calculators only have buttons for log base 10 and natural log, so the formula converts any other base into one of those.
The formula is log base b of x equals log base c of x divided by log base c of b, for any valid new base c.
The proof follows directly from the definition of a logarithm and the power rule of logarithms.
Practicing with numeric bases like log base 2 of 20 builds the skill needed for solving logarithmic equations later.
What You'll Practice
1
Rewriting logarithms in multiple equivalent forms using different bases
2
Calculating decimal values of logarithms with bases other than 10
3
Evaluating expressions with coefficients and complex arguments like fractions and radicals
4
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:
This Unit Includes
7 Video lessons
Practice exercises
Learning resources
Skills
Change-of-Base Formula
Logarithms
Calculator Skills
Exponential Form
Equation Solving
Algebraic Manipulation
OH Curriculum Aligned