What is the inverse function of #f(x) =10^x#?

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Answer 1 · 2015-10-23T15:27:02

#y =log_(10)(x)#

Let #" " y = 10^x#

Take logs of both sides giving:

#ln(y) =ln(10^x)#

Or better still use log to base 10 giving:

#log_(10)(y) =log_(10)(10^x)#

But #log_(10)(10^x) = x times log_(10)(10)#

and #log_(10)(10) = 1#

Giving:

#log(y) = x#

Now swap #x# and #y# around giving

#y =log_(10)(x)#