Question

Помогите со степенями! 10-11класс

Answer 1

$10^{3}* (\frac{1}{10})^{ \frac{1}{x} }=10 x^{2x} \\ \frac{10^{3} }{10 ^{ \frac{1}{x} } } =10^{2x} \\ 10^{3- \frac{1}{x} =10 ^{2x} \\ 3- \frac{1}{x}=2x$
$2 x^{2} -3x+1=0 \\ x=1,x= \frac{1}{2}$
2.$2 ^{x}=2 ^{-5x+6} \\ x=-5x+6 \\ 6x=6 \\ x=1$
3. $3^{4 \sqrt{x} }=3^{2x-6} \\ 4 \sqrt{x} =2x-6 \\ \left \{ {{x>3} \atop {16x=4 x^{2} +36-24x}} \right. \\ \left \{ {{x>3} \atop {4 x^{2} -40x+36=0}} \right. \\ \left \{ {{x>3} \atop {(x=1,x=9)}} \right. \\ x=9$

Answer 2

решение во вложениях
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