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Solving for a variable in an algebra equation with logs and powers

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#algebra-precalculus #logarithms #exponentiation
50
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Solving for a variable in a complex algebra equation with logs and powers

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#algebra-precalculus #logarithms #exponentiation
234
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Solve $i^{i^{i^\ldots}}$

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#complex-numbers #exponentiation #tetration #power-towers
516
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Is $f(z)=2^z$ a homomorphism?

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#complex-analysis #complex-numbers #field-theory #exponentiation #group-homomorphism
1.6k
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Why does the approximation for exponents $(a+b)^c \approx a^{c-bc} (a+1)^{cb}$ work?

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#exponential-function #exponentiation #approximation
1.1k
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How can I solve $x^\sqrt{y} +y^\sqrt{x} =\dfrac{49}{48}$ and $\sqrt{x}+\sqrt{y} =\dfrac72$?

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#numerical-methods #systems-of-equations #exponentiation #radicals
363
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GCD and exponentiation of large numbers

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#exponentiation #gcd-and-lcm
2.2k
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What is the best algorithm for finding the last digit of an enormous exponent?

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#elementary-number-theory #modular-arithmetic #exponentiation #big-numbers
91
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Limits of ${\int\limits_{-\infty}^\infty f(x)e^x\mathrm{d}x}$ changed to $(0,\infty)$ if $f(x)$ is even

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#integration #definite-integrals #improper-integrals #exponentiation #even-and-odd-functions
241
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How many solutions to each of the equations $2^x+3^y=5^z$, $2^x+5^y=3^z$, $3^x+5^y=2^z?$

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#diophantine-equations #exponentiation
67
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Is there a law for summing powers of logarithms?

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#summation #logarithms #exponentiation
233
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Reversing digits of power of 2 to yield power of 7

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#number-theory #modular-arithmetic #exponentiation
101
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Solve for a variable with a variable exponent.

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#logarithms #exponential-function #exponentiation
479
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Solve power with negative exponent $\frac{125^{6}\times 25^{-3}}{(5^{2})^{-3}\times25^{7}}$

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#algebra-precalculus #exponentiation
165
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$2^{3^{4^{...^{n}}}} \equiv 1$ (mod $n+1$)

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#elementary-number-theory #modular-arithmetic #exponentiation #power-towers

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