Solve-log-2x-2-log-3x-2-log-2-2-log-3-2-

Question Number 121899 by ZiYangLee last updated on 12/Nov/20

Solve {(\log 2 x)}^{2} + {(\log 3 x)}^{2} = {(\log 2)}^{2} + {(\log 3)}^{2}

Commented by Dwaipayan Shikari last updated on 12/Nov/20

x = 1

2 {l o g}^{2} x + 2 l o g 2 l o g x + 2 l o g 3 l o g x = 0

{l o g}^{2} x + l o g x l o g 6 = 0

l o g x = - l o g 6 \Rightarrow x = \frac{1}{6} o r l o g x = 0, x = 1

Commented by ZiYangLee last updated on 12/Nov/20

thanks sir

Answered by MJS_new last updated on 12/Nov/20

{(\log n x)}^{2} = {(\log x)}^{2} + 2 \log n \log x + {(\ln n)}^{2}

transforming the given equation we get

\log x \log (6 x) = 0

\Rightarrow x = 1 \lor x = \frac{1}{6}

Commented by ZiYangLee last updated on 12/Nov/20

Thanks sir . . ★