# Log help.

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• Aug 19th 2009, 05:00 PM
el123
Log help.
$\displaystyle \log_{8}x^{\frac{3}{2}} - \log_{8}x^{\frac{1}{2}}$

Can some one please tell me how i work this out.
• Aug 19th 2009, 05:09 PM
skeeter
Quote:

Originally Posted by el123
$\displaystyle \log_{8}x^{\frac{3}{2}} - \log_{8}x^{\frac{1}{2}}$

Can some one please tell me how i work this out.

$\displaystyle \log(a) - \log(b) = \log\left(\frac{a}{b}\right)$
• Aug 19th 2009, 05:19 PM
el123
thanks , what if the question says , that the equation equals 2.

and gives me multiples answers to choose what x is. The answer is 64......i dont know why. Could you explain to me the process i go through to get that answer.
• Aug 19th 2009, 05:34 PM
skeeter
Quote:

Originally Posted by el123
thanks , what if the question says , that the equation equals 2.

and gives me multiples answers to choose what x is. The answer is 64......i dont know why. Could you explain to me the process i go through to get that answer.

$\displaystyle \log_8{x^{\frac{3}{2}}} - \log_8{x^{\frac{1}{2}}} = 2$

$\displaystyle \log_8\left(\frac{x^{\frac{3}{2}}}{x^{\frac{1}{2}} }\right) = 2$

$\displaystyle \log_8{x} = 2$

change to an exponential equation ...

$\displaystyle 8^2 = x$

$\displaystyle 64 = x$

in future, please post the entire question from the start.