Question

Log 1/100,000 describe why your answer is correct

Answer 1

log(1/100000) = -5

The answer is correct because when we take 10 to the (-5)th power, we get 1/100000

i.e.
`10^(-5)=1/100000`

Explanation:

We know that log(a) means asks about to what power should we take 10 to get "a" as a result, or, for the equation,

`10^x=a`

Here, what does x have to be such that 10^x will be equal to a, in log form,

`log(10^x)=log(a)\\x = log(a)`

Now, in our case, a = 1/100000

so, the equation is,

x = log(1/100000)

Now, since

`10^1 = 10, 10^0 = 1, 10^(-1)=1/10, 10^(-2)=1/100,10^(-3)=1/1000,\\10^(-4)=1/10000,10^(-5)=1/100000\\\\10^(-5)=1/100000`

So, we see that x = -5 or,

log(1/100000) = -5

The answer is correct because when we take 10 to the (-5)th power, we get 1/100000