Simplifying and/or Computing problems

killasnake · #1 $Old$ October 2nd, 2007, 10:20 AM

Hi I need help simplifing these problems.

1. 2ln $sqrt(e)$
= $sqrt(3)^2$
= 3

2 $^Logx$ = 2^log4 x
= 4 $^3x$

3. tan $^-1$ (1/ $sqrt(3)$
= pi/3

are these right?

topsquark · #2 $Old$ October 2nd, 2007, 10:38 AM

Quote:

Originally Posted by killasnake $View Post$

1. 2ln $sqrt(e)$
= $sqrt(3)^2$
= 3

Where did the 3 come from?

$2~ln(\sqrt{e}) = 2~ln \left ( e^{1/2} \right ) = 2~ \frac{1}{2} \cdot ln(e) = 1 \cdot 1 = 1$

-Dan

topsquark · #3 $Old$ October 2nd, 2007, 10:46 AM

Quote:

Originally Posted by killasnake $View Post$

2 $^Logx$ = 2^log4 x
= 4 $^3x$

I presume "Log" is $log_{10}$ ?

Use the change of base formula:
$log_{10}(x) = \frac{log_2(x)}{log_2(10)}$

So
$2^{log_{10}(x)} = 2^{\frac{log_2(x)}{log_2(10)}}$

$= \left ( 2^{log_2(x)} \right )^{1/log_2(10)}$

$= x^{1/log_2(10)} \approx x^{0.30103}$

-Dan

topsquark · #4 $Old$ October 2nd, 2007, 10:48 AM

Quote:

Originally Posted by killasnake $View Post$

3. tan $^-1$ (1/ $sqrt(3)$
= pi/3

Close.
$tan^{-1} \left ( \frac{1}{\sqrt{3}} \right ) = \frac{\pi}{6}$

-Dan

killasnake · #5 $Old$ October 2nd, 2007, 10:51 AM

Quote:

Originally Posted by topsquark $View Post$

Where did the 3 come from?

$2~ln(\sqrt{e}) = 2~ln \left ( e^{1/2} \right ) = 2~ \frac{1}{2} \cdot ln(e) = 1 \cdot 1 = 1$

-Dan

oh crap i just realised my problem... the 3 was suppose to be an e