If-3x-2-e-log-x-27-27000-then-find-x-

Question Number 74006 by necxxx last updated on 17/Nov/19

I f 3 x^{2} e^{\log_{x} 27} = 27000 t h e n f i n d x

Commented by necxxx last updated on 17/Nov/19

p l e a s e h o w c a n t h i s b e s o l v e d a n a l y t i c a l l y

o r e v e n b y n u m e r i c a l m e t h o d s =

p l e a s e h e l p

Answered by MJS last updated on 17/Nov/19

3 x^{2} e^{\frac{\ln 27}{\ln x}} = 27000

x^{2} \times 27^{\frac{1}{\ln x}} = 9000

x = e^{t}

27^{\frac{1}{t}} e^{2 t} = 9000

2 t + \frac{3 \ln 3}{t} = \ln 9000

t^{2} - \frac{\ln 9000}{2} t + \frac{3 \ln 3}{2} = 0

t = \frac{\ln 9000}{4} \pm \sqrt{\frac{{(\ln 9000)}^{2}}{16} - \frac{3 \ln 3}{2}}

t_{1} \approx . 396518

t_{2} \approx 4.15597

x = e^{t}

x_{1} \approx 1.48664

x_{2} \approx 63.8139

Commented by necxxx last updated on 17/Nov/19

w o w \dots . I r e a l l y d i d n t t h i n k t h i s w a y .

w h a t s w r o n g w i t h m y b r a i n ? ?

I^{'} m j u s t s o g r a t e f u l s i r M J S

Commented by MJS last updated on 17/Nov/19

{you}^{'} re welcome

we all are prejudiced sometimes and cannot

see the obvious \dots

Facebook Tweet Pin