Question

$(sqrt(10)-3)^2^x=(sqrt(10)+3)$

Answer 1

$sqrt{10}+3=dfrac{(sqrt{10}+3)(sqrt{10}-3)}{sqrt{10}-3}=dfrac{10-9}{sqrt{10}-3}=(sqrt{10}-3)^{-1}$

 

$(sqrt{10}-3)^{2x}=(sqrt{10}-3)^{-1}$

$2x=-1$

$x=-dfrac12$