Question

Помогите,пожалуйста, с показательным уравнением !
3* 4^х + 2* 9^х = 5* 6^х

Answer 1

$frac{3 times {2}^{2x} }{ {3}^{2x} } - frac{5 times {2}^{x} times {3}^{x} }{ {3}^{2x} } + frac{2 times {3}^{2x} }{ {3}^{2x} } = 0$
$3 ( { frac{2}{3}) }^{2x} - 5( { frac{2}{3}) }^{x} + 2 = 0$
$( { frac{2}{3}) }^{x} = ( frac{2}{3} ) \ x = 1 \ ( { frac{2}{3} )}^{x} = 1 \ x = 0$

Answer 2

$3*4^{x}+2*9^{x}=5*6^{x}\\3*frac{4^{x} }{9^{x} }-5*frac{6^{x} }{9^{x} }+2*frac{9^{x} }{9^{x} }=0\\3*(frac{2}{3})^{2x}-5*(frac{2}{3})^{x}+2=0\\(frac{2}{3})^{x}=m,m>0$

$3m^{2}-5m+2=0\\D=(-5)^{2}-4*3*2=25-24=1\\m_{1}=frac{5+1}{6}=1\\m_{2}=frac{5-1}{6} =frac{2}{3}$

$1)(frac{2}{3})^{x}=1\\(frac{2}{3} )^{x}=(frac{2}{3})^{0} \\x_{1}=0\\2)(frac{2}{3})^{x}=frac{2}{3}\\x_{2} =1$