How do you find the inverse of an exponential function?

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Answer 1 · 2017-11-23T11:51:16

See explanation about 'inverse function'.

Suppose we have: #y=a^x#

Take logs of both sides

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

But #ln(a^x)# is the same as #xln(a)# giving:

#ln(y)=xln(a)#

Divide both sides by # ln(a)#

#ln(y)/ln(a)=x#

Now swap round the letters #x and y# giving:

#ln(x)/ln(a)=y#

#y=ln(x)/ln(y)#