How do you calculate # log 0.00007#?

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Answer 1 · 2016-06-15T19:41:08

You can apply the scientific notation and the properties of the logarithms.

First of all

#0.00007 = 7*10^-5#.

Then

#log(0.00007)=log(7*10^-5)#

now we apply the rule #log(a*b)=log(a)+log(b)#

#log(7*10^-5)=log(7)+log(10^-5)#

and finally we use the property that #log(a^b)=b*log(a)#

#log(7)+log(10^-5)=log(7)-5log(10)#.

Now I do not know if #log# is with base #e# or base #10#.
If it is base #e# the result is #-9.57# otherwise it is #-4.15#.