Log Function and Exponent Precedence

[eurythmistan]

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^xe

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!

 

[Curious3141]

The short answer is: avoid ambiguous expressions. Even if you think precedence is well-established, misunderstandings can occur. Use parentheses freely, or just arrange the expression more intelligently.

 

[Mark44]

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

I don't see that the two expressions above are different, unless you mean the second to be (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^xe

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!

It looks like wolfram and TI have different rules for determining operator precedence. As Curious3141 says, the best thing to do is to write expressions unambiguously so that there will be no confusion. For your trig example, here's what I mean:
[sin(pi/4]]² vs. sin((pi/4)²).

 

[eurythmistan]

Totally makes sense, thanks!

This was actually a question posed to me by someone else, and I tried to say something similar to what you both did, but you both said it so much better. Thanks again!