query: Solution to equation $2^x $ = $x^8$
positive_passages.docid: 17265
positive_passages.text: Intuition for why equations of the form $k^x=x^c$ are not solvable trivially?
negative_passages.docid: 62161
negative_passages.text: Solutions of the Pell-type equation $x^2-2y^2=-1$
negative_passages.docid: 68164
negative_passages.text: $(2x^2+3y^2-7)xdx-(3x^2+2y^2-8)ydy=0$
negative_passages.docid: 83909
negative_passages.text: Is $2^{2n} = O(2^n)$?
negative_passages.docid: 149254
negative_passages.text: Solving $y^3=x^3+8x^2-6x+8$
negative_passages.docid: 41782
negative_passages.text: Real Solution of $4^x + 6^x = 9^x$.
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$
negative_passages.docid: 61022
negative_passages.text: Diophantine Equations : Solving $a^2+ b^2=2c^2$
negative_passages.docid: 124581
negative_passages.text: Solving $x^2 - 1 = e^x$
negative_passages.docid: 62446
negative_passages.text: Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$
negative_passages.docid: 94700
negative_passages.text: Integer solutions for $x^3+2=y^2$?
negative_passages.docid: 87304
negative_passages.text: Solving for $x$ : $a^x+b^x=c$
negative_passages.docid: 139051
negative_passages.text: Pell type equation: $x^2-py^2=a$
negative_passages.docid: 144851
negative_passages.text: For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
negative_passages.docid: 135074
negative_passages.text: How do you solve this equation?
negative_passages.docid: 43476
negative_passages.text: An exponential equation over positive real numbers $4^x+14^x+3^x=11^x+10^x$
negative_passages.docid: 34059
negative_passages.text: $(a^{2^n}+1,a^{2^m}+1)=1 or 2$