How solve this $\log { { x }^{ \log _{ x }{ y } } } =\quad \frac { 5 }{ 2 } \\ x+y=6\\ $

Question

How solve this logarithm equation

$\log { { x }^{ \log _{ x }{ y } } } =\quad \frac { 5 }{ 2 } \\ x+y=6\\ $

score 1 · Accepted Answer · answered Mar 02 '14 at 09:18

1

Hint

$\log _{ x }{ y }=\frac{\log (y)}{\log (x)}$ then $\log { { x }^{ \log _{ x }{ y } } }=\log (y)$

I am sure that you can take from here.

answered Mar 02 '14 at 09:18

Claude Leibovici

Or more simply, $\log_x(y)$ is by definition a number $t$ such that $x^t = y$. – Robert Israel Mar 02 '14 at 09:20

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