Question

Помогите пожалуйста решите 2 и 4 , желательно фото решения

Answer 1

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

$4)27^{5-x^{2}}=3^{x^{2}-1} \\\\(3^{3}) ^{5-x^{2}}=3^{x^{2}-1}\\\\3^{15-3x^{2}}=3^{x^{2}-1}\\\\15-3x^{2}=x^{2}-1\\\\4x^{2}=16\\\\x^{2} =4\\\\\boxed{x_{1}=-2;\\x_{2} =2}$

Answer 2

$2)\\1.5^{x} * ((\frac{3}{2})^{-1})^{2x-1} = 1\\1.5^{x}*1.5^{-2x+1} =1\\1.5^{x-2x+1} =1\\1.5^{-x+1} =1\\1.5^{-x+1} =1.5^{0} \\-x+1=0\\x=1$

4)

$(3^{3})^{5-x^{2}} =3^{x^{2} -1} \\3^{15-3x^{2}} =3^{x^{2} -1} \\15-3x^{2} =x^{2} -1\\4x^{2} = 16\\x^{2} =4\\x_{1} =2 \\x_{2} =-2$