# Combine the equation into a single logarithm

• December 10th 2010, 10:39 PM
SilvaNoctix
Combine the equation into a single logarithm
1/4log˅br + 2log˅bs -2/3log˅bt

i multipled the first two terms and divided the last one from the to get an answer of log˅b r^1/4s^2/t^2

is this the correct approach and answer?
many thanks.
• December 10th 2010, 10:46 PM
Sudharaka
Quote:

Originally Posted by SilvaNoctix
1/4log˅br + 2log˅bs -2/3log˅bt

i multipled the first two terms and divided the last one from the to get an answer of log˅b r^1/4s^2/t^2

is this the correct approach and answer?
many thanks.

Dear SilvaNoctix,

Do you mean, $\displaystyle\log_{b}\left(\frac{r^{\frac{1}{4}}s^ 2}{t^{\frac{2}{3}}}\right)$ ??
• December 10th 2010, 10:55 PM
SilvaNoctix
yes, sorry, i'm not used to writing equations on this site yet. That's exactly what i meant though... is it the correct answer?
• December 10th 2010, 11:05 PM
Sudharaka
Quote:

Originally Posted by SilvaNoctix
yes, sorry, i'm not used to writing equations on this site yet. That's exactly what i meant though... is it the correct answer?

Yes it is correct. If you have used the logarithm rules,

$\log (A\timesB)=\log A+\log B$

$\log \left(\frac{A}{B}\right)=\log A-\log B$

$\log A^{n}=n\log A$

.....then the approach is also correct.