query: Find all real number satisfying $10^x+11^x+12^x = 13^x+14^x$
positive_passages.docid: 79241
positive_passages.text: Solve $10^x+11^x+12^x = 13^x+14^x$
negative_passages.docid: 106934
negative_passages.text: $x^x=y$. How to solve for $x$?
negative_passages.docid: 68960
negative_passages.text: How to solve $ 13x \equiv 1 ~ (\text{mod} ~ 17) $?
negative_passages.docid: 50995
negative_passages.text: infinitude of primes that are $11 \bmod 12$
negative_passages.docid: 119691
negative_passages.text: $5^{x}+2^{y}=2^{x}+5^{y} =\frac{7}{10}$ Work out the values of $\frac{1}{x+y}$
negative_passages.docid: 85653
negative_passages.text: $2^x + 3^x - 4^x + 6^x - 9^x ≤ 1$ $\forall x \in R$
negative_passages.docid: 100759
negative_passages.text: Extending exponentiation to reals
negative_passages.docid: 110460
negative_passages.text: find remainder of a number
negative_passages.docid: 133430
negative_passages.text: How to solve $x^x=100$?
negative_passages.docid: 118314
negative_passages.text: How to define $x^a$ for arbitrary real numbers $x$ and $a$
negative_passages.docid: 66861
negative_passages.text: Show that $11^{10} \equiv 1 (\mod 100)$
negative_passages.docid: 17609
negative_passages.text: Finding the remainder of $11^{2013}$ divided by $61$
negative_passages.docid: 147470
negative_passages.text: Divisibility of Consecutive Powers of 10
negative_passages.docid: 110958
negative_passages.text: How to solve for any given natural number n?
negative_passages.docid: 103993
negative_passages.text: Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
negative_passages.docid: 49899
negative_passages.text: Determine the number of real roots
negative_passages.docid: 48053
negative_passages.text: Show that 13 divides $2^{70}+3^{70}$