3ln(x^2)-2ln(x 1/3) +4ln(x-1)=1 ,solve for x:
anyone?

Question

anonymous · Answer

Is the problem$$3\ln(x^{2})-2\ln(x^{\frac{1}{3}})+4\ln(x-1)=1$$?

anonymous · Answer

yeah@alex

anonymous · Answer

do you need real solutions or all solutions? exact solutions?

anonymous · Answer

Real Solution in Exact Form: x = 1/6 (3+sqrt(3 (3+4 sqrt(3) e^(1/4))))

anonymous · Answer

how did u get that?

anonymous · Answer

wait is that x to the 1/3

anonymous · Answer

$$3lnx^2-2lnx^{\frac{1}{3}}+4\ln(x-1)=1$$$$lnx^{6}-lnx^{\frac{2}{3}}+\ln(x-1)^4=1$$$$\ln \frac{x^6}{x^{\frac{2}{3}}}+ln(x-1)^4=1$$$$\ln x^{\frac{16}{3}}+\ln(x-1)^4=1$$$$\ln[x^{\frac{16}{3}}\times(x-1)^4]=lne$$$$[x^{\frac{16}{3}}\times(x-1)^4]=e$$I'm too lazy to complete it, sorry.

kira_yamato · Answer

I'll leave you with the basic logarithm from here...

anonymous · Answer

thnkuu so much kira..

anonymous · Answer

Kira - How did you make a picture like that?

kira_yamato · Answer

Screenshot...

anonymous · Answer

Of what? MathType, or similar? Sorry for being inquisitive, but that was nice. xD

kira_yamato · Answer

I used equation editor... But you can use MathType if you like... It's the same...