Question

25^{1-3х} =\frac{1}{25}

3^{х\frac{1}{2}} * 3^{х-2} = 1

16^{х} +4^{х}-2 = 0
5^{х+1} - 5^{х-2}=620

Answer 1

1)

$25^{1-3x}= \frac{1}{25} \\ \\ 5^{2-6x}=5^{-2} \\ \\ 2-6x=-2 \\ \\ -6x=-4 \\ \\ x= \frac{2}{3}$

2)

$3^{x* \frac{1}{2}}*3^{x-2}=1 \\ \\ 3^{ \frac{3}{2}x-2}=3^0 \\ \\ \frac{3}{2}x-2=0 \\ \\ \frac{3}{2} x=2 \;\; \mid *(2) \\ \\ 3x-4=0 \\ \\ 3x=4 \\ \\ x= \frac{4}{3}$

3)

$16^x+4^x+2-2=0 \\ \\ (4^x)^2+4^x-2=0 \\ \\ 3AMEHA: t=4^x \\ \\ t^2+t-2=0 \\ \\ Za \;\; Vieta: \\ \\ t=1 \\ 1=-2 \\ \\ 4^x=1 =\ \textgreater \ 4^x=4^0=\ \textgreater \ x=0\\ x^x=-2 \;\;\;Ne \;\; vozmoshno \\ \\ \boxed {x=0}$

4)

$5^{x+1}-5^{x-2}=620 \\ \\ (5^3-1)*5^{x-2}=620 \\ \\ 124*5^{x-2}=620 \mid \;\; \div (124) \\ \\ 5^{x-2}=5 \\ \\ x-2=1 \\ \\ \boxed {x=3}$