Log Help

[JVP13]

Hey Everyone,

Struggling to rearrange to solve for x in the attached image, my logs are a bit rusty. Answer is supposed to be around 16.5 but i am not having any luck.

If anyone is able to provide some assistance that would be much appreciated.

Thanks

Josh

 

[Quaid]

Struggling to rearrange to solve for x in the attached image, my logs are a bit rusty. Answer is supposed to be around 16.5 but i am not having any luck.

If anyone is able to provide some assistance that would be much appreciated.

Hi Josh:

This particular equation cannot be solved by hand, easily. I played around with it, but always ended up in one of two situations; x is isolated on one side, but trapped inside a log input on the other side, or, x is isolated on one side, but trapped in the exponent position on the other side.

I think you need a numerical approach, to estimate the solution. One such is graphing each side, and zooming in on the intersection point.

The equation is equivalent to x/10 = (10 - x/2)^(25/27)

Another approach is to use equation-solving software, like WolframAlpha, which gives the approximatation x=16.5532 and shows the graph of each side (as well as expressing the exact solution in terms of a root of a 27th-degree polynomial containing huge coefficients).

Cheers