# Logs

• May 20th 2009, 08:44 AM
aimeemcdonald
Logs
Log10(x)=ylog10(3)+1
express y in terms of x

help?
explaination needed though
• May 20th 2009, 10:35 AM
earboth
Quote:

Originally Posted by aimeemcdonald
Log10(x)=ylog10(3)+1
express y in terms of x

help?
explaination needed though

$\log_{10}(x)=y \cdot \log_{10}(3) + 1$

$\log_{10}(x)-1=y \cdot \log_{10}(3)$

$\log_{10}\left(\dfrac x{10}\right)=y \cdot \log_{10}(3)$

$\dfrac{\log_{10}\left(\dfrac x{10}\right)}{\log_{10}(3)}=y$

which can be simplified to:

$y = \log_3\left(\dfrac x{10} \right)$