# Thread: Reverse Second Order Logrithm

1. ## Reverse Second Order Logarithm

Hi all

I hopw this is the correct forum for this post, but here goes.

I have the following equation :-

$y=a+b*log(x) + c*log(x)^2$

This basically describes the power conversion efficiency from AC Watts input (x) to DC Watts output (y) for a power supply.

I need to reverse the equation so that I can find the AC Watts input (x) from the DC Watts output (y).

This has got me stumped

Cheers

Andy

2. Originally Posted by Duckfather
Hi all

I hopw this is the correct forum for this post, but here goes.

I have the following equation :-

$y=a+b*log(x) + c*log(x)^2$

This basically describes the power conversion efficiency from AC Watts input (x) to DC Watts output (y) for a power supply.

I need to reverse the equation so that I can find the AC Watts input (x) from the DC Watts output (y).

This has got me stumped

Cheers

Andy
Let u= log(x). Then your equation is $y= a+ bu+ cu^2$. Solve that with the quadratic formula and then $x= 10^u$ (I am assuming that your log is the "common log" to base 10).