# Tagged Questions

For question involving exponential functions and questions on exponential growth or decay.

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### Three almost-integers of the form $ce^{H_a+H_b}\approx 2^k\pm1$

The approximation $$H_n\approx log(2n+1)$$ http://math.stackexchange.com/a/1602945/134791 suggests that the harmonic number for composite odd numbers might be close to the sum of the harmonic ...
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### Evaluating an integral that contains a positive definite matrix

Let $A \in \mathbb{R}^{d \times d}$ be a positive definite matrix (meaning that $z^t A z > 0 \space \forall z \in \mathbb{R}^d, z ≠ 0$, although I'm also allowed to use any other of the "usual" ...
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### Unable to process Large numbers [closed]

A small spherical cell of diameter $1.616E^{-35}$ is exponentially multiplying as $2^n$ where n is the generation number. The duration of 1 generation is $5.39E^{-44}$ second. And the cells cluster ...
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### A circle centered at the origin is tangent to $y=2^x$. What is the radius of the circle?

I feel as though I am doing the analytical part correctly, however, where I am facing the roadblocks in this problem is in the actual algebra itself. Perhaps I am not doing something right in my ...
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### how do you solve exponential equations with added bases

im confused on how you solve a question like this: $$3^{x+2} + 3^{x-1} = 27$$ would you do: $$2(3)^{2x}-1 = 3^3$$ but when I try this way its wrong, please help me thanks.
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### If $f(z)$ is meromorphic but not entire, is $\exp(f(z))$ meromorphic? Could it even be entire?

First, I can show that $f$ meromorphic is a rational function. Now, I want to consider $g=e^{f(z)}$. I have heard that there is something interesting that goes on with $g$, that there is some room ...