# log problem

• Mar 27th 2010, 03:42 AM
mastermin346
log problem
solve the following equation

$\displaystyle \log_{\sqrt x}16-\log_{\sqrt x}2=3$
• Mar 27th 2010, 04:24 AM
skeeter
Quote:

Originally Posted by mastermin346
solve the following equation

$\displaystyle \log_{\sqrt x}16-\log_{\sqrt x}2=3$

use this property of logarithms on the left side of the equation ...

$\displaystyle \log_a{m} - \log_a{n} = \log_a\left(\frac{m}{n}\right)$

... then convert the resulting log equation to an exponential equation and solve for x.
• Mar 27th 2010, 04:48 AM
Subcydian
$\displaystyle \log_{\sqrt{x}}8 = 3$

$\displaystyle \sqrt{x} ^ {log_{\sqrt{x}}8} = \sqrt{x} ^ 3$

$\displaystyle 8 = x ^ \frac{3}{2}$

$\displaystyle x = 8 ^ \frac{3}{2}$

$\displaystyle x = 4$
• Mar 27th 2010, 06:37 AM
skeeter
Quote:

Originally Posted by Subcydian
$\displaystyle \log_{\sqrt{x}}8 = 3$

$\displaystyle \sqrt{x} ^ {log_{\sqrt{x}}8} = \sqrt{x} ^ 3$

$\displaystyle 8 = x ^ \frac{3}{2}$

$\displaystyle x = 8 ^ \frac{3}{2}$

$\displaystyle \textcolor{red}{x = 8^{\frac{2}{3}}}$

$\displaystyle x = 4$

...