Question

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

Answer 1

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=`