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Showing posts from August, 2015

Maths: Which One Is Bigger, 1000^1001 or 1001^1000?

The question is as such: $1000^1001$❓$1001^1000$ ⬆️ We want to find the❓operator. Well, not... "we" per se. You might think — WHY am I involved in this? 🤔 I'm not obliged to solve that, am I? — Indeed. Do excuse me. Let me rephrase that. I want to find the ❓ operator. Mwahahaha. It's the reasonind behing this post. 🦹 Right. So. I scribbled that using logarithmic . Here it goes. The Scribble $1000^1001❓1001^1000$ Let me assume: $1000 = a$ Therefore: $1001 = (a + 1)$ So this: $1000^1001❓1001^1000$ Becomes: $a^(a+1)❓(a + 1)^a$ ➡️ I then place log (logarithmic function) on both sides. This form: $a^(a+1)❓(a + 1)^a$ ➡️ Becomes: $log_a$ $(a^(a+1))$ $❓$ $log_a$ $((a + 1)^a)$ Continue by implementing — logarithmic properties. The form above can be transformed into this: $(a + 1) log_a(a)❓(a) log_a(a + 1)$ I can simplify $log_a(a) = 1$. Thus: $(a + ...
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