log 0.06

Question

log 0.06

zehanz · Answer

If you write it as $\log\dfrac{6}{100} $, you can use the rule: $\log\dfrac{a}{b}=\log a - \log b$.

zehanz · Answer

But if you only need to know an approximation, you can type it into a calculator, of course...

anonymous · Answer

no i have to do it without a calculator and have no idea how!

anonymous · Answer

so can i just put log3-log50?

zehanz · Answer

You could use the method I described above. 
One of the two logs can be calculated, the other one stays as it is...

anonymous · Answer

log3-log50
which one stays as it is though?

zehanz · Answer

No, although 6/100=3/50, that is not convenient here.
I would write it as: $\log6 - \log 100$, then I can see what log 100 is...can you?

anonymous · Answer

zehanz · Answer

Mine seems like a "second opinion"  :)
It is not different than @dpaInc's...

anonymous · Answer

second time around, it prolly be correct... :)

anonymous · Answer

@dpaInc , i submitted that and she said it was not right.

zehanz · Answer

Well, is there an explanation given then? 
Are there rules you have to apply?

zehanz · Answer

You could write log 6 as log 2 + log 3, but it doesn't get simpler if you do.

anonymous · Answer

you can simplify (or use the log rules again) log(6) = log(3*2) = ???

anonymous · Answer

i dont think so, i will go back and check though to make sure!
isnt log 100 =2?

zehanz · Answer

It is!

anonymous · Answer

okay, this is exactly what i sent her(i ad to show work)
log(0.06)=log(6/100)=log(6)−log(100)=log(6)−2

zehanz · Answer

That is what we came up with.

The only thing you could do further, is: 

log(0.06)=log(6/100)=log(6)−log(100)=log(2*3)−2=log(2)+log(3)-2

anonymous · Answer

thanks guys, i will try that!