How to Graph Logarithms (Logs) Using Transformations

Learn two powerful methods to graph logarithms using transformations! Mario's Math Tutoring demonstrates how to graph y = log_2(3 - x) + 1 by first identifying the parent function and then applying sequential transformations (shifts and reflections). Alternatively, discover a second method: rewriting the logarithmic equation in its equivalent exponential form (x = 2^(y-1) - 3) and plotting points by choosing values for y. Understand how to identify the vertical asymptote, a key feature of logarithmic graphs.

In this video, you'll discover:

0:00 Introduction to Graphing Logarithms Using Transformations
0:30 Method 1: Graphing Using Transformations
0:40 Identifying the Parent Function (y = log_2(x))
1:00 Rewriting Parent Function in Exponential Form (x = 2^y)
1:15 Creating a Table of Values for the Parent Function
2:00 Graphing the Parent Function
2:30 Transformation 1: Horizontal Shift (x + 3 inside log) - Shifts Left 3
3:30 Graphing the Shifted Function
4:00 Transformation 2: Reflection (-x inside log) - Reflects over Y-axis
5:00 Graphing the Reflected Function
5:30 Transformation 3: Vertical Shift (+1 outside log) - Shifts Up 1
6:00 Graphing the Final Transformed Function and Identifying the Vertical Asymptote
6:50 Method 2: Rewriting in Exponential Form
7:00 Rearranging the Equation to Isolate the Logarithm
7:20 Exponentiating Both Sides to Convert to Exponential Form
8:00 Solving for x (x = -2^(y-1) + 3)
8:30 Creating a Table of Values by Plugging in y and Solving for x
9:10 Graphing the Exponential Form and Identifying the Vertical Asymptote
Master graphing logarithmic functions using both transformation and exponential form methods!

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