Question

calculati:

3^x * 2^(x+3) = 288

coronita!!

Answer 1

$Il~descompunem~pe~288~in~produs~de~factori~primi. \\ \\ 288=2 \cdot 144=2 \cdot 12^2=2 \cdot (3 \cdot 4)^2 =2 \cdot 3^2 \cdot 2^4=2^5 \cdot3^2. \\ \\ Deci~3^x \cdot 2^{x+3}=3^2 \cdot 2^5. \\ \\ Evident~x \geq 0.~x=0~nu~convine,~deci~x\ \textgreater \ 0. \\ \\ In~acest~caz~3^n \neq 2^m,~deci~egalitatea~are~loc~daca~3^x=3^2~si~ \\ \\ 2^{x+3}=2^5. \\ \\ Solutie:~\boxed{x=2}~.$