What is the inverse of #y=log( -3x) +2?# ?

1 Answer
Nov 12, 2015

Given:
#y=log(-3x)+2#

#log(-3x) =y-2#

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Consider the case of# " "log_10(6) = b#
This means that #10^b = 6#

When you see just #" "log("of something") " "# it is understood to mean log to base 10.
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So now we have #10^(y-2) = (-3)x#

Thus we have #x=-(10^(y-2))/3#

Now interchange the variables of #x# and #y# to give:

#y=-(10^(x-2))/3#

If you we to incorporate logs now you would end up with #log(y)=# which is not the same as #y=#