- Lasha Kokilashvili
Visual proof of the property logM + logN = log(M*N)
Write down the answers to the following questions on a piece of paper: 1. Looking at the graph of the function f, how is the value of Y1 defined in terms of u? Double click with your mouse on y1, appearing in the algebra window and answer: 2. How is y2 related to y2? 3. How is y3 related to y2? How is y3 related y1? 4. Using the Quotient Property of two powers with the same base, check that M=a^(v-u) 5. Using to the definition of logarithm, what does v-u equal to? what does w-v equal to? And what about w-u? 6. Looking at the three line segments [u,v], [w-v] and [w-u] in the drawing, determine how they are related. 7. Keeping in mind the three expressions found when answering questions in 5, and relationship found in 6, what can you conclude about three logarithms? 8. Use the sliders to interact with the applet, does the relation you discovered above (when answering questions in 6 and 7) change? 9. Right click on the parameter a (i.e. the base of the exponential function f) and try to change its value to something reasonable (e.g. set a=2), and use sliders again. 10. What can you conclude?