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

Answer 1

Sophie Adams

#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)#

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Answer 2

Benjamin Achtenberg

The inverse function of ( f(x) = 10^x ) is ( f^{-1}(x) = \log_{10}(x) ), also written as ( f^{-1}(x) = \log(x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.