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How to prove "if $2^x=2^y$ so $x=y$"

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#logarithms #exponentiation
37
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Sum of n with factoral exponent

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#exponentiation
90
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Highest power of 4 that divides n

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#exponentiation #integers
137
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What went wrong in proving $i=1$

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#complex-numbers #exponentiation #radicals #fake-proofs
62
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What happens when a is negative in $ a^{\frac{m}{n}} $.

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#exponentiation
180
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Addition of different bases raised to the same power (solve for power). Is power determined uniquely?

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#linear-algebra #number-theory #vector-spaces #power-series #exponentiation
537
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Properties and applications of complex logarithms and exponentials.

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#complex-analysis #complex-numbers #logarithms #exponentiation
40
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Determine all real (a,b,c) that satisfy the systems of equations.

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#prime-numbers #systems-of-equations #exponentiation
57
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How do I express $y = 1 - e^{-ax^b}$ as a linear function in terms of $y$, $x$, $a$, and $b$?

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#logarithms #exponentiation
100
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How to show this rule works for whole numbers to the fifth power?

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#arithmetic #recreational-mathematics #exponentiation
390
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Find $f^{−100}g^{146}f^{301}$ (permutations to high powers)

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#proof-writing #permutations #exponentiation #permutation-cycles
44
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0 to the power of any number

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#proof-verification #exponentiation
50
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Optimum way of self replication?

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#self-learning #exponentiation
113
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How to calculate $n$ in $f = p^n - q^n$?

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#exponentiation
66
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Prove that every number to a power greater than 1 can be written as $X^{n+1} = \Sigma_{i=1}^{n}(a_{i}X^{i}-b_{i}Y^{i})$

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#number-theory #exponentiation #natural-numbers

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