query: How is $\ a^{\log_nb} = b^{\log_na} $?
positive_passages.docid: 30835
positive_passages.text: Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$
negative_passages.docid: 113526
negative_passages.text: Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?
negative_passages.docid: 132366
negative_passages.text: Diagonalizability of $A \in M_{n}(\Bbb{R})$ (Upper traingular matrix) with all diagonal entries 1 and $A \neq I$?
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 127290
negative_passages.text: Intuition behind logarithm change of base
negative_passages.docid: 126859
negative_passages.text: $\Bbb Z^\ast$ What is this notation?
negative_passages.docid: 98439
negative_passages.text: In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
negative_passages.docid: 101519
negative_passages.text: What is the condition for example $(number^c)^b=number^{cb}$ to be true?
negative_passages.docid: 48081
negative_passages.text: Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 131844
negative_passages.text: When does $(e^a)^b = e^{ab}$ hold?
negative_passages.docid: 28520
negative_passages.text: Exponential or logarithm of a dimensionful quantity?
negative_passages.docid: 85186
negative_passages.text: Basic demonstration concerning the natural logarithm...
negative_passages.docid: 113394
negative_passages.text: What does O(log n) mean exactly?
negative_passages.docid: 46780
negative_passages.text: Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
negative_passages.docid: 41534
negative_passages.text: A system of logarithmic equations with parameters
negative_passages.docid: 46556
negative_passages.text: How to prove $3^{\log_4n} = n^{\log_43}$?