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Compute $\lim \limits_{x \to \infty} \frac{(2x+3)^x-3^x}{2^x-3^x}$ without L’Hospital’s rule

How can I compute $$\lim\limits_{x\to\infty}\frac{(2x+3)^x-3^x}{2^x-3^x}$$ without L’Hospital’s rule?

$(\forall x\ge 1)$ $(2x+3)^x=e^{x\log(2x+3)}$.
We have $-x\log(2x+3)\ge \log(2x+3)-1\ge\log3$.
Thus, $(\forall x\ge 1)$ $(2x+3)^x-3^x\le\exp(\log3-x\log(2x+3))-3^x=(3-2\log3)\exp(\log3-x\log(2x+3))$.
Now, $\lim_{x\to\infty}(3-2\log3)\exp(\log3-x\log(2x+3))=3-2\log3$ and hence $\limsup_{x\to\infty}(2x+3)^x-3^x\le 3-2\log3$.

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After i attach the game media (ex: dvd, cd), I insert it into the drive, then press play and it just says [No sound driver] and then the game sound is totally off. Everytime I try to make a new game media (and put it in a different drive), it still says the same thing. I don’t know what to do. Please help me.1. Field of the Invention
The present invention relates to an image recording material, more specifically to a silver halide photographic material having improved tone gradation.
2. Description of the Prior Art
Various photographic techniques have heretofore been known. For example, with silver chlorobromide emulsions which are tabular in crystal habit, (hereinafter referred to as tabular emulsions) can be obtained photographic properties such as high sensitivity, excellent sharpness, improved covering power and improved gradation, even in a color photographic paper. On the other hand, silver halide emulsions (hereinafter referred to as non-tabular emulsions) of relatively high aspect ratio (the ratio of grain size to grain thickness) can be obtained by use of a hard gradation control or by forming a large number of emulsion grains.
However, there has been a problem in such conventional silver halide photographic materials which are improved in gradation such as the above described tabular emulsions, that are produced are only one type of emulsion. It is believed that tabular grains cannot be produced with the aforementioned technique when they are mixed with conventional emulsions. Furthermore, there is a serious problem in these conventional tabular emulsions because they tend to deteriorate their photographic properties when stored for a long period of time.
On the other hand, with conventional non-tabular emulsions, it is well known that the photographic properties thereof tend to deteriorate when stored for a long period of time. Also, conventional large-grain emulsions have insufficient covering power and/or high fog.
Furthermore, there is a problem in the conventional

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