Answer
$(\sqrt 10, 10)$
Work Step by Step
Given the system of equations:
1. $\log x + \log y = 3/2$
2. $2\log x - \log y = 0$
The question asks to find all real solutions.
Add equations 1 and 2
$\log x + \log y = 3/2$
+ ($2\log x - \log y = 0$)
$3\log x = 3/2$
$\log x = 1/2$
$x = 10^{1/2} = \sqrt 10$
Substitute the values into the equation
$\log (10^{1/2}) + \log y = 3/2$
$1/2 + \log y = 3/2$
$\log y = 1$
$y = 10$
All Solutions:
$(\sqrt 10, 10)$
