solve-for-x-1-3-log-x-3-log5-log-x-2-2-0-

Question Number 42627 by mondodotto@gmail.com last updated on 29/Aug/18

solve for x

\frac{1}{3} \log (x - 3) + \log 5 - \log {(x - 2)}^{2} = 0

Answered by $@ty@m last updated on 30/Aug/18

\log (x - 3) + 3 \log 5 - 3 \log {(x - 2)}^{2} = \log 1

\frac{125 (x - 3)}{{(x - 2)}^{6}} = 1

{(x - 2)}^{6} = 125 x - 375

x^{6} - 6 x^{5} . 2 + 15 x^{4} . 2^{2} - 20 x^{3} . 2^{3}

+ 15 x^{2} . 2^{4} - 6 x . 2^{5} + 2^{6} = 125 x - 375

x^{6} - 12 x^{5} + 60 x^{4} - 160 x^{3} + 240 x^{2}

- 317 x + 439 = 0

t o b e c o n t i n u e \dots

Answered by ajfour last updated on 30/Aug/18

\frac{125 (x - 3)}{{(x - 2)}^{6}} = 1

125 (x - 3) - {(x - 2)}^{6} = 0

\Rightarrow x \approx 3.008, x \approx 4.351 .

Commented by mondodotto@gmail.com last updated on 30/Aug/18

thank you sir