Question

Решите уравнение: x^lg9+9^lgx=6

Answer 1

$x^{lg9} = x^{ \frac{log_{x}9}{log_{x}10} } =(x^{log_{x}9})^{ \frac{1}{log_{x}10}} =9^{lgx}$
$9^{lgx}+9^{lgx}=6$
$2*(9^{lgx}) = 6$
$9^{lgx} = 3$
$3^{2lgx}=3^1$
$lgx = \frac{1}{2}$
$x = \sqrt{10}$

Answer 2

X^log(b)a=a^log(b)x⇒
x^lg9=9^lgx
9^lgx+9^lgx=6
2*9^lgx=6
9^lgx=3
lgx=1/2
x=√10