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Why can $\int_{x=0}^{\infty} x\,\mathrm{e}^{-\alpha x^2}\mathrm {d}x$ not be evaluated by parts to obtain $\frac{1}{2\alpha}$?

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#calculus #integration #definite-integrals #exponentiation #gaussian-integral
482
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How do I convince students in high school for which this equation: $2^x=4x$ have only one solution in integers that is $x=4$?

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#real-analysis #logarithms #education #exponentiation
199
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Simplification of $n^{1/\sqrt{\log n}}$

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#functions #exponentiation
39
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Will the absolute logarithm always produce the correct real result if one exists?

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#logarithms #exponentiation #absolute-value
27
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What kind of operation/rule was applied here?

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#exponentiation
148
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$p^3 = 2009 + 47 * 2^q$ where p and q are primes

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#number-theory #prime-numbers #modular-arithmetic #exponentiation
68
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Exponentiation involving high powers of 2.

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#algebra-precalculus #exponentiation
25
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Simple way to generate a sequence where the 1st number is $x_1$, the tenth number is $x_{10}>x_1$ and the 20th number is above some order of magnitude

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#sequences-and-series #exponentiation
1.2k
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Comparing Large Exponents with different bases.

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#logarithms #arithmetic #exponentiation
495
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repeated exponents sign

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#notation #exponentiation
109
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Is the following solvable for x?

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#exponential-function #exponentiation #lambert-w
15.7k
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X raised to power-X raised to power-3 equals to 3.

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#algebra-precalculus #number-theory #elementary-number-theory #exponentiation
389
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Last two digits of $3^{7^{2016}}$

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#elementary-number-theory #modular-arithmetic #exponentiation
25.7k
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Limit of a function raised to a power

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#limits #exponentiation
787
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Calculate the power, given all other numbers in an equation

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#exponentiation

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