GRE question about logs

Asked Feb 26 '21 at 19:51

Active Feb 26 '21 at 19:51

Viewed 138 times

So I have a question about a step they make in the GRE subject book.

Finding derivative of $\arcsin($log$(x)))$

So I know how to do it, its just chain rule but there's one step I really do not understand:

they go from

$$(\log(\sqrt{e}))^2=\frac{1}{4}$$

I get that

$$\log(\sqrt{e}) = \frac{1}{2}\log e$$

but I thought

$$\ln e=1$$

and that regular log of $e$ is like .4 something...

Am I missing something?

asked Feb 26 '21 at 19:51

homosapien

2

$\log$ is commonly used to denote $\ln$. – player3236 Feb 26 '21 at 19:53
ok thanks! that clears things up a lot. Not a fan of this ambiguity. – homosapien Feb 26 '21 at 19:53
1

I am assuming that the author let $\log = \log_e =\ln$. Then
$$(\log(\sqrt{e}))^2=(\log e^{1/2})^2=\left(\frac12 \log e\right)^2=\left(\frac 12\right)^2 = \frac 14$$
– Axion004 Feb 26 '21 at 19:59
1

@HossienSahebjame Most math books will use $\log$ instead of $\ln$, whereas the opposite is true for physics/engineering. – rubikscube09 Feb 26 '21 at 20:00
yes as apposed to base $10$, thought the same after @player3236 said that – homosapien Feb 26 '21 at 20:00
@rubikscube09 thanks! – homosapien Feb 26 '21 at 20:01

0 Answers0