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

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