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Logarithmic Riddle
February 26, 2021
On Friday February 26, just before his bedtime, Mortaza came to my room and asked me to let him play solitaire card game on my computer. I told him he could play one game. After he finished, he asked me to let him play one more time. I told him, if he wrote me a math riddle that took me more than one minute to solve, I would let him play again. Then he wrote this math riddle for me.
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I was surprised to see the logarithm notation. Since I had never talked to him about logarithm before, and since he wrote it incorrectly, I assumed that he was playing, which was not like Mortaza. I told him this was logarithm and whether he knew what it meant. His answer: "It is the opposite of power." He then gave me an example. Then I asked him where he learned about it. He said from the calculator. And then in response to my question of "how," he showed me on the scientific calculator of his iPad, when he raised a number to the power of another number repeatedly, and then took the logarithm of the result in a similar base repeatedly, we got back to the original number. 
The fact that he learned about log from a calculator explained the weird notation that he used in his riddle, since this was similar to the sequence of the key stroke to calculate the logarithm of a number. So, in fact he meant this:
Of course, he used the wrong base for the logarithm. So, I explained to him the right way of writing the logarithm, which in turn meant that he needed to make adjustment to his riddle. 
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Later, to test whether he understood the concept, I gave him this riddle, which he solved quickly and correctly. 
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Since he managed to solve the above riddle with utmost ease, I gave him a series of more challenging logarithmic problems over the next couple of days, which he solved without too much difficulty.
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Revisiting logarithms (April 16-2021)
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