Question

Rezolvati ecuatia :
$2^{3^{x} } =3^{2^{x} }$

Answer 1

2^3^x = 3^2^x

= log2 (2^3^x) = log2 (3^2^x) ;

iar folosind firmula: a (a^x) =x,

Si formula log a (b^c) = c × log a(b), inlocuim

=> 3x = 2^x × log2 (3)

=> 3x = log2 (3) × 2^x

Acum, impartim ecuatia cu 2^x

( 3) ^x

__ = log2 (3)

(2)

Si acum scoatem logaritmul din ecuatie

=log 3÷2 ((3÷2)^x) = log 3÷2 (log2 (3))

=> x = log 3÷2 (log2 (3))