12 questions linked to/from Display Log with desired notation in output
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### How to simplify logs but keep the same base [duplicate]

Consider the function: $f(x)=\log_3x+\log_316-\log_34$. This can be simplified to $\log_34x$. To simplify this function in Mathematica, I would use the command ...
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### Mathematica Sec and Csc

How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"? In Germany these functions are "old fashioned" as they are not taught anymore at school.
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### Replacing Tan[x] with Sin[x]/Cos[x]

Why doesn't this work? (1 - Tan[x])/(Sin[x] - Cos[x]) /. Tan[x] -> Sin[x]/Cos[x] I get back: ...
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### Simplify Sin[x]/x to Sinc[x]

I have an expression in the form of $\tt \frac{Sin[x]}{x}$ that I would like to simplify to the form of Sinc[x]. I've tried the ...
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### How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
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### How to rename a built-in function?

I want a built-in function renamed without loss of any properties, I want the shorter name to appear in all results and to be recognized as input. Is it possible?
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### Prevent manipulations in PlotLegends

Mathematica code to reproduce: ...
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### How do I convert the E^[…] notation back to Exp[…] notation?

How do I convert the E^[...] notation back to Exp[...] notation? Is there a simple command for this? It appears that ...
4.*^-12 Sqrt[3.0254210421890627*^22 - 6.25*^22 T6^2] The above expression is equal to Sqrt[0.48406736675024997 - T6^2] ...