Question

What is the inverse of `y=log(3x-1)`?

Answer 1

`y=(log(x)+1)/3`

See the explanation

Explanation:

The objective is to get only `x` on one side of the `=` sign and everything else on the other. Once that is done you change the single `x` to `y` and all the `x's` on the other side of the `=` to `y`.

So first we need to 'extract' the `x` from `log(3x-1)`.

By the way, I assume you mean log to base 10.

Another way of writing the given equation is to write it as:

`10^(3x-1)=y`

Taking logs of both sides

`log(10^(3x-1) )= log(y)`

but `log(10^(3x-1))` may be written as `(3x-1) times log(10)`

and log to base 10 of 10 = 1
That is: `log_10(10) =1`

So no we have

`(3x-1) times 1 = log(y)`

`3x =log(y) +1`

`x= (log(y) +1)/3`

Change the letters round

`y=(log(x)+1)/3`

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