Question

9^log(10)*x+x^log(10)*9=6​

Answer 1

$9^{\log_{10}x}+x^{\log_{10}9}=6$

По свойству $a^{\log_{b}c}=c^{\log_ba}$ имеем:

$9^{\log_{10}x}+9^{\log_{10}x}=6;\\\\2\cdot9^{\log_{10}x}=6;\\\\9^{\log_{10}x}=3;\\\\3^{2\log_{10}x}=3^1;\\\\2\log_{10}x=1;\\\\\log_{10}x=0.5;\\\\x=10^{0.5};\\\\x=\sqrt{10}.$

ОТВЕТ: $\sqrt{10}$