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A diophantine equation with unknown exponents: $ 4^n + 5^n = 7^m + 2^m $
exponential-function
diophantine-equations
integers
Find all $x\in\mathbb{R}$ such that $\left( \sqrt{2-\sqrt{2} }\right)^x+\left( \sqrt{2+\sqrt{2} }\right)^x=2^x$.
algebra-precalculus
exponential-function
exponentiation
monotone-functions
Proof of the inequality $e^x\le e^{x^2} + x$ [duplicate]
inequality
exponential-function
The matrix exponential: Any good books?
matrices
reference-request
exponential-function
book-recommendation
The image of a horizontal line Im(z)=pi/4 for the complex number f(z)=e^z
complex-analysis
exponential-function
graphing-functions
Why is $(10/x)^x$ biggest when $10/x = e$?
real-analysis
calculus
optimization
exponential-function
maxima-minima
Fake proof that $\frac{e^x-1}{e^x+1}=e^x$, via integrating $\operatorname{sech} x$ in two ways
integration
trigonometry
exponential-function
fake-proofs
Stirling's formula Baby Rudin
analysis
logarithms
exponential-function
gamma-function
change-of-variable
Evaluate $\lim\limits_{n\rightarrow\infty}\left(\frac{n^2 + 1}{n^2 - 2}\right)^{n^2}$
limits
exponential-function
eulers-number-e
How to prove $(\frac{n+1}{e})^n<n!<e(\frac{n+1}{e})^{n+1}$ without integrating method?
inequality
exponential-function
factorial
Why the number e(=2.71828) was chosen as the natural base for logarithm functions? [duplicate]
logarithms
exponential-function
How does one solve for $x$ in the equality $a^x = bx + c$?
inequality
logarithms
exponential-function
special-functions
lambert-w
How to compute time ordered Exponential?
matrices
ordinary-differential-equations
multivariable-calculus
exponential-function
matrix-calculus
Is $e^x=\exp(x)$ and why?
calculus
notation
definition
exponential-function
Solve equation $\exp(ax)+\exp(bx)=1$
exponential-function
transcendental-equations
prove that $\frac{1-e^{-x^2}}{x}\le 2\sqrt{2} , \ x>0$,
calculus
algebra-precalculus
inequality
exponential-function
Solve an equation with linear and exponential functions, $x=10^{x/10}$ [closed]
algebra-precalculus
exponential-function
Find the number of natural solutions of $5^x+7^x+11^x=6^x+8^x+9^x$
calculus
real-analysis
functions
exponential-function
karamata-inequality
Prove this limit without using these techniques, and for beginner students: $\lim_{x\to0} \frac{e^x-1-x}{x^2}=\frac12$
calculus
limits
exponential-function
limits-without-lhopital
Find $\lim_{x\to-\infty}{x+e^{-x}}$
limits
exponential-function
infinity
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