How do you find the inverse of #y=log( -3x) +2#?

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Answer 1 · 2016-03-05T17:33:14

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

Have you have used the word 'log' I am assuming you are talking about #log_10#

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

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

Note that #log(a)=b" "->" "10^b=a#

#=>log(-3x)=y-2" "->" "10^(y-2)=-3x#

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

Now swap the letters #x" and "y# around giving:

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

#color(green)("This should be a reflection of the original equation about "#
#color(green)(y=x)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B