Question

Прошу, помогите. нужно срочно

Answer 1

$2^{3x-1}+25^{x}\cdot 2^{x-1}=125^{x}\\\\2^{3x}\cdot 2^{-1}+5^{2x}\cdot 2^{x}\cdot 2^{-1}=5^{3x}\; |:5^{3x}\\\\( \frac{2}{5})^{3x}\cdot 2^{-1}+(\frac{2}{5})^{x}\cdot 2^{-1}=1\; |\cdot 2\\\\(\frac{2}{5})^{3x}+( \frac{2}{5})^{x} =2\\\\t=( \frac{2}{5} )^{x}\ \textgreater \ 0\; ,\; \; \; t^3+t-2=0\; ,$

$t_1=1\; \; -\; koren,\; t.k.\; \; \; 1^3+1-2=0\\\\t^3+t-2=(t-1)(t^2+t+2)=0\\\\t^2+t+2=0\; ,\; \; D=1-4\cdot 2=-7\ \textless \ 0\; \; \Rightarrow \; \; net\; dejstvitelnux\; kornej\\\\(\frac{2}{5})^{x}=1\; \; \to \; \; ( \frac{2}{5})^{x} =(\frac{2}{5})^0\\\\x=0$