Question

Anyone here !!


....


If able to solve the following problems !!


Plzz solve it !!

It's a HUMBLE REQUEST !


As it's VERY IMPORTANT ND URGENT !!
PLZZ!


Thanks!!

Regards
LEGENDARY QUEEN! ​

Answer 1

$heya \\ \\ 6)\\ \\ 3 {}^{2x} \times 3 {}^{4} + 1 = 2 \times 3 {}^{x} \times 3 {}^{2} \\ \\ \\ divide \: both \: sides \: by \: \: 3 {}^{x} we \: get \\ \\ \\ 3 {}^{x} \times 3 {}^{4} + 3 {}^{ - x} = 2 \times 3 {}^{2} \\ \\ \\ \\ \\ 81 \times 3 {}^{x} + 3 {}^{ - x} = 18 \\ \\ \\ \\ put \: \: 3 {}^{x} = z \\ \\ \\ \\ 81z + 1 \div z \: \: \: = 18 \\ \\ \\ 81z {}^{2} + 1 = 18z \\ \\ \\ \\ 81z {}^{2} - 18z + 1 = 0 \\ \\ \\ \\ 81z {}^{2} - 9z - 9z + 1 = 0 \\ \\ \\ 9z(9z - 1) - 1(9z - 1) = 0 \\ \\ \\ (9z - 1)(9z - 1) = 0 \\ \\ \\ \\ (9z - 1) = 0 \\ \\ \\ z = 1 \div 9 \\ \\ \\ z = 3 {}^{ - 2} \\ \\ \\ \\ so \\ \\ \\ \\ 3 {}^{x} = 3 {}^{ - 2} \\ \\ \\ \\ x = - 2$