Question

Could you help me with this? (log(x) base 3)^2=(log(x^2) base sqrt(3)) + (log(9) base sqrt(3)), solve by x.

Answer 1

If you can solve it, just give me the final solution please:)

Answer 2

I am just confirming..
Is x = root(3)/2 ???

Answer 3

No, it's not:(

Answer 4

Then what is it??

Answer 5

if log(x) with base root(3) = 2log(x) with base 3, then solution is 3^(2+-2root(2))

Answer 6

but i'm not sure about that rule so i asked if you guys could help...

Answer 7

\(\large log^2_3x = log_{\sqrt3}x^2+log_{\sqrt3}9 \)
solve for x?

Answer 8

The following is correct
\[\log_{\sqrt{3}} x=2\log_{3} x\]

Answer 9

\[(\log_{3} x)^{2}=\log_{\sqrt{3}} x ^{2}+\log_{\sqrt{3}}9 \]
\[(\log_{3} x)^{2}-4\log_{3} x-4=0\]The solution to the quadratic is
\[\log_{3} x=2\pm2\sqrt{2}\]

Answer 10

Thanks a lot:)