Graph of Exponential 2^x | Real Numbers | Class 10 TG | Mathematics | Khan Academy скачать в хорошем качестве

Graph of Exponential 2^x | Real Numbers | Class 10 TG | Mathematics | Khan Academy

Course Link:- https://www.khanacademy.org/math/clas... What happens when the answer to a power isn't a whole number? If 2^x = 8, we know x=3, but what if 2^x = 5? In this video, we explore the behavior of the exponential function y = 2^x and discover the tool designed to find these "hidden" exponents: the Logarithm. We build a table of values and plot the Exponential Curve, observing how it shoots up toward infinity and has a horizontal asymptote at y = 0. Finally, we bridge the gap between exponentials and logarithms, showing you how to translate between the two forms (a^x = N into log_a N = x) and introducing Common Logarithms (base 10). Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! Timestamps: 0:00 - Intro Puzzle: Solving for 2^x = 8 0:14 - The Mystery: What if 2^x = 5? 0:34 - Building the Table of Values for y = 2^x 1:25 - Plotting the Exponential Curve 2:14 - The Horizontal Asymptote (y = 0) 2:27 - Key Observations: Exponential Growth 2:40 - Using the Graph to Estimate x for y = 5 3:02 - Entering Logarithms: The Inverse Operation 3:34 - Connecting Exponents and Logs: 2^3 = 8 vs. log2 8 = 3 4:52 - Solving Examples: 1/4, 1/2, and More 7:46 - Generalizing the Rule: a^x = N 8:52 - Special Case: Common Logarithms (Base 10) 9:32 - Summary and Key Takeaways Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate