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! #GraphingLogarithms #LogarithmicFunctions #Transformations #ExponentialForm #VerticalAsymptote #Algebra2 #Precalculus #MathTutorial #MathHelp Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below) https://www.mariosmathtutoring.com/fr... ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)    / @mariosmathtutoring