#1**+1 **

OOOH ! I got one...it requires more than just logarithm knowledge though!

**Be warned!** I spent a VERY LONG time on this and never got the answer

But....you asked for it....here it is:

3log(x - 2) = log(2x) - 3

hectictar
May 29, 2017

#2**+2 **

3log ( x - 2) = log (2x) - 3

Note that we can write 3 as log (1000)

So we have

3 log (x - 2) = log (2x) - log (1000) and we can write

log ( x - 2)^3 = log [ (2x) / 1000]

log ( x - 2)^3 = log (x / 500) we can forget the logs and solve for

(x - 2)^3 = ( x / 500) simplify

x^3 - 6x^2 + 12x - 8 = x / 500 multiply both sides by 500

500x^3 - 3000x^2 + 6000x - 4000 = x subtract x from both sides

500x^3 - 3000x^2 + 5999x - 4000 = 0 difficult to solve this, algebraically....

WolframAlpha shows the real solution as

x ≈ 2.1629

CPhill
May 29, 2017