What is the inverse of #y=6^x#?

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Answer 1 · 2016-06-27T04:30:23

#x=log_6y#

Since

#x=log_ba iff a=b^x#

you have:

#y=6^x iff x=log_6y#

Answer 2 · 2016-06-27T04:30:32

#y= (ln x)/(ln 6)#

Replace x with y and y with x,

# x= 6^y# and solve for y now

ln x= yln 6

#y= (ln x)/(ln 6)#

Answer 3 · 2017-07-18T10:40:33

See below.

If #g(x)# is the inverse for #f(x)# then

#g(f(x))=x# then

#g(6^x)=x rArrg(x) = log_ex/log_e 6 = f^-1(x)#.