# help with logarithm question,please help

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• October 7th 2009, 05:10 AM
silvermist
help with logarithm question,please help
given that log2 (3)=m and log2 (5)=n express log2 (0.15) in terms of m and n

i'm sorry if your guys dont understand but i'll type it in words just to make sure

log three base two is equals to m........log five base two is equal to n......

sorry its hard to type the base of the log
• October 7th 2009, 05:38 AM
Raoh
Hello(Wink)
$\frac{\ln 3}{\ln 2}=m,\frac{\ln 5}{\ln 2}=n\Leftrightarrow \ln 2=\frac{\ln 5}{n}=\frac{\ln 3}{m}\Leftrightarrow \frac{1}{\ln 2}=\frac{m}{\ln 3}=\frac{n}{\ln 5}$.
$\Leftrightarrow$ $\frac{\ln 0.15}{\ln 2}=\frac{\ln 0.15\times m}{\ln 3}=\frac{\ln 0.15\times n}{\ln 5}$,therefore $\log_{2}0.15=m\log_{3}0.15=n\log_{5}0.15$.