# Natural Logarithm

are they equal?

#### BvU

Homework Helper
The first is hard to recognize, but I would take them both as the fourth power of the natural logarithm of (x+3).

The fact they use ln instead of log is decisive.

The first notation is to be avoided: there are already two notations for the base of a logarithm: $^e\log y$ and $\log_e y$ for $\ln y$ and this looks too much like a third notation for the same, which it is NOT.

#### funlord

when i tried it on symbolab.com i subtract them both and i'd come up with answer of 0

does that mean they are equal?

#### BvU

Homework Helper
I don't acknowledge that kind of authority in a website. But yes, they are equal for the reason that they describe one and the same thing: the fourth power of the natural logarithm of (x+3).

#### funlord

ok, thank you very much

#### Mark44

Mentor
The first notation is to be avoided: there are already two notations for the base of a logarithm: $^e\log y$ and $\log_e y$ for $\ln y$ and this looks too much like a third notation for the same, which it is NOT.
Just for the record, I have never seen this notation -- $^e\log y$. By "never" I mean in the past 55+ years. That's not to say that someone hasn't used it somewhere, but if so, it's certainly not in common usage. The notation $\log_e y$ is rarely used, since $\ln y$ is defined to mean log, base e, of y.

If someone were to write $\log^4 (x + 3)$, I would interpret this to mean the same as $(\log(x + 3))^4$ following the usual shorthand as used in powers of trig functions. I would also interpret the log base to be 10, but in some contexts the implied log base could be e or possibly 2, in computer science textbooks.

#### BvU

Homework Helper
Just for the record, I have never seen this notation -- $^e\log y$. By "never" I mean in the past 55+ years. That's not to say that someone hasn't used it somewhere, but if so, it's certainly not in common usage. The notation $\log_e y$ is rarely used, since $\ln y$ is defined to mean log, base e, of y.

If someone were to write $\log^4 (x + 3)$, I would interpret this to mean the same as $(\log(x + 3))^4$ following the usual shorthand as used in powers of trig functions. I would also interpret the log base to be 10, but in some contexts the implied log base could be e or possibly 2, in computer science textbooks.
I now miss how you DO write $^4\log 16 = 2$ ? With the rarely used notation ?

Writing $^4\log 16$ is pretty common in Europe...

Ah, wait, of course $^e\log y$ is rarely used because $\ln y$ exists. In fact $\log y =\ ^e\log y\$ for a lot of decent people (mathematicians, for one) !

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving