решите уравнение: x^lg9+9^lgx=6. Created by Whithoutme. algebra-ru

решите уравнение: x^lg9+9^lgx=6...

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

17 votes Thanks 28

sedinalana 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

3 votes Thanks 2

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