# logarithm help! - write as single quantity

• Oct 21st 2009, 10:21 AM
snypeshow
logarithm help! - write as single quantity
Hey guys! I need help with this question:

Write the expression as a logarithm of a single quantity

http://img97.imageshack.us/img97/979/259006.gif

I know to make any of it computable in a calculator, the logs need to be in base10. but i'm not sure how to do it because of a, b & c.
• Oct 21st 2009, 10:33 AM
masters
Quote:

Originally Posted by snypeshow
Hey guys! I need help with this question:

Write the expression as a logarithm of a single quantity

http://img97.imageshack.us/img97/979/259006.gif

I know to make any of it computable in a calculator, the logs need to be in base10. but i'm not sure how to do it because of a, b & c.

Hi snypeshow,

Use these basic logarithm properties:

$\displaystyle \log_bx+\log_by=\log_b(xy)$

$\displaystyle \log_bx-\log_by=\log_b\left(\frac{x}{y}\right)$

$\displaystyle 3\log_5a+4\log_5b-2\log_5c=(\log_5a^3+\log_5b^4)-\log_5c^2=$

$\displaystyle \log_5(a^3b^4)-\log_5c^2=\boxed{\log_5\left(\frac{a^3b^4}{c^2}\ri ght)}$