Exponential equation

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sadovnichek

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Joined
Dec 17, 2020
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Hi everyone.

I want to solve the next equation:
[math]2^{n} = n + 2[/math]
I don't know how to get complete solution. First, I try to solve with graphical method and find one root - it's n = 2. The second one placed between (-2, -1.5). Then I began an analytical solution and stuck again:
[math]\log_{2}(2^n) = \log_{2}{(n + 2)}[/math][math]n = \log_{2}{(n + 2)}[/math]???
Any ideas?
 
sadovnichek said:
Hi everyone.

I want to solve the next equation:
[math]2^{n} = n + 2[/math]
I don't know how to get complete solution. First, I try to solve with graphical method and find one root - it's n = 2. The second one placed between (-2, -1.5). Then I began an analytical solution and stuck again:
[math]\log_{2}(2^n) = \log_{2}{(n + 2)}[/math][math]n = \log_{2}{(n + 2)}[/math]???
Any ideas?
Click to expand...
What's n's domain? Real, Integer, Complex...?
 
You have n in the base and n in the exponent in the same equation. Sometimes the answers can be seen my inspection, but no algebraic manipulation will work.
 
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