- #1

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## Homework Statement

This isn't really a specific problem, just a question if hand-writing log functions (or trig functions) is interpreted differently than when typing them into a calculator or something like Wolfram Alpha.

Suppose you have this on paper:

ln e

^{x}

Is this the same as both of the expressions below?

ln (e

^{x})

ln (e)

^{x}

This is what you get, when you enter what I think are equivalent expressions to each of those, onto a calculator (or wolfram)

ln (e^x) ===> x

ln (e^1)^x ===> 1

But I guess my question is, is this really the way you'd interpret the above expressions, if you saw them written out?

I thought that if you wanted the ln function taken to a power, you'd write these, for example:

(ln e)

^{x}

ln

^{x}e

If you do something similar with sine, then wolfram and my TI-82 calculator differ in their interpretations:

sin(pi/4)^2 =

.5 (according to wolfram)

.5785... (according to ti-82)

I'm wondering if this is a case where there isn't really one specified standard, or if I'm doing something wrong?

Any insight will be appreciated, thank you!