# How do you calculate #antilog 0.3010 #?

##### 1 Answer

Jun 19, 2016

#### Answer:

#### Explanation:

The function:

#f(x) = 10^x#

is one to one and strictly monotonically increasing on its domain

It therefore has an inverse with domain

#g(x) = log x#

which is also one to one and strictly monotonically increasing.

Hence the inverse of

So both of the following hold:

#log(10^x) = x# for all#x in (-oo, oo)#

#10^log(x) = x# for all#x in (0, oo)#

So:

#anti log 0.3010 = 10^0.3010 ~~ 1.9998618696#

Alternatively, if you know:

#log 2 ~~ 0.30102999566#

then:

#2 ~~ anti log 0.30102999566 ~~ anti log 0.3010#