if log 2=.301and log 3=.477, what is the approximate value of log 108?

Question

zolock · Answer

24 = 3 × 8 = 3 × 2³ 
log 24 = log 3 + 3 log 2 
0.477 + 0.903 = 1.38 

These are approximate logs to base 10, by the way 

More accurate value of log10 24 = 1.38021124171

anonymous · Answer

$$108=2^2\times 3^3$$ is a start

anonymous · Answer

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kc_kennylau · Answer

One formula for you: $\log a+\log b=\log ab$

anonymous · Answer

is the a  2 and the b 3?

accessdenied · Answer

You should have this in mind...  You have approximate values for log 2 and log 3.  They ask you to approximate log 108.  So, you want to break log 108 apart using logarithm rules so that the only thing left over is log 2 and log 3 in terms of logarithms.  Then you can make the approximation happen.

example:    If you were approximating 144, you could say:  144 = 2*72.  Thus, log(144) = log (2*72) = log 2 + log 72.   Now you have a log 2 which you know approximates to be .301.  Reduce the log(72) further to make more progress...