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Why is $ a^x = e^{x \log a} $?

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#logarithms #exponentiation
98
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If $2^a=3^b$ find $\frac{a}{b}$

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#algebra-precalculus #logarithms #exponentiation
83
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Why is $a^{-x}$ defined to be equal to $\frac{1}{a^x}$?

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#exponentiation
344
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How do I solve for $x$ in $ab^x-cd^x=e$?

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#exponential-function #exponentiation
743
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Finding the inverse of my f(x) function that includes a fractional exponent (with a variable in the fraction)

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#logarithms #exponentiation #inverse-function
110
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Calculating $\lim\limits_{j \to \infty} \frac{j^{j/2}}{j!}$

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#real-analysis #calculus #limits #exponentiation #limits-without-lhopital
599
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How to express 80^2/3 as a product of powers of prime numbers

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#exponentiation #prime-factorization
63
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Is there a shorter way to say "b raised to the n-th power"

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#exponentiation
89
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General formula of $\lim_{n \to \infty} (1+a_n)^{b_n}$ where $b_n \to \infty$

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#sequences-and-series #limits #exponential-function #exponentiation
61
Views

What is the base of this exponent?

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#notation #exponentiation
93
Views

A problem in algebra: how does $-1=1$?

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#exponentiation
112
Views

$(-1)^3$ has different results when evaluated as $(-1)\times(-1)\times(-1) = -1$ vs $((-1)^2)^{3/2} = 1$. Which is correct?

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#arithmetic #exponentiation #fractions
36
Views

How to write $12 (N / m)^2$ in long form

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#exponentiation
212
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Connection between powers of $i$ and derivatives of $\sin$ and $\cos$?

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#complex-analysis #derivatives #trigonometry #exponentiation
55
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Show whether or not the functions $f(x,y)=|x|^y$, $g(x,y)=|x|^{|1/y|}$ have limits at $(0,0)$.

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#real-analysis #limits #multivariable-calculus #exponentiation

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