Here's something nontraditional:

\(2^x-3^{x/2}-1=0\)

We can guess or use W|A to figure that \(x=2\). But can we crack this problem analytically?

This problem arose out of Karim Mohamed's solution to Big Problem, small solution.

Here's something nontraditional:

\(2^x-3^{x/2}-1=0\)

We can guess or use W|A to figure that \(x=2\). But can we crack this problem analytically?

This problem arose out of Karim Mohamed's solution to Big Problem, small solution.

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TopNewestDo you mean finding a general solution in terms of functions?(logarithms for example) or just approximating and finding number of solutions???? – Hasan Kassim · 2 years, 9 months ago

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Thanks – John Muradeli · 2 years, 9 months ago

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A non-rigorous proof would be to note how

\[2^x-3^{x/2}\]

grows larger and larger as \(x\) increases. A quick table would quickly confirm. If we let \(y=2^x-3^{x/2}\), we have:

\((2, 1)\),

\((4, 5)\),

\((6, 37)\),

\((8, 175)\),

and so on and so forth. – Finn Hulse · 2 years, 9 months ago

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Oh, maths.

Thanks, Finn. – John Muradeli · 2 years, 9 months ago

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\(2.71828^x-6.67384^{x/2}-360=0\)?

Try making tables now. – John Muradeli · 2 years, 9 months ago

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