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How to Graph Logarithmic Functions
See exactly how to graph logarithmic functions like y = log x and y = ln x, plus how to spot the asymptote, intercept, and shape of every log curve.
What You'll Learn
Every logarithmic graph has a vertical asymptote and passes through the point (1, 0), since log base b of 1 is always 0
The graph of y = log x rises slowly when the base is greater than 1 and falls when the base is between 0 and 1
The natural log graph, y = ln x, behaves the same way as any log curve but uses base e and passes through (e, 1)
Transformations such as y = log base b of (x minus h) plus k shift the asymptote and key points the same way they do for other functions
Because log and exponential functions are inverses, the log graph is a reflection of the exponential graph across the line y = x
What You'll Practice
1
Plotting logarithmic functions using tables of values
2
Converting between logarithmic and exponential forms
3
Finding asymptotes, domain, range, and intercepts from graphs
4
Graphing log functions with base 2 and base 1/2
5
Comparing inverse relationships between exponential and logarithmic functions
Why This Matters
Graphing logarithmic functions is essential for understanding exponential relationships in reverse, which you'll encounter in science, finance, and engineering. Mastering these graphs helps you solve exponential equations, analyze decay and growth models, and prepares you for calculus and higher-level math courses.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Logarithms
Graphing
Exponential Form
Inverse Functions
Asymptotes
Domain and Range
Transformations
OH Curriculum Aligned