Question

aflati valoarea lui x : a) 3.3 la a 3 . 3 la a 5 . 3 la a 7 . ....... 3 la 21 = 3 la 11 la x

Answer 1

    
$3=3^1 \\ 3^1\cdot3^3\cdot3^5\cdot3\cdot~........~\cdot3^{21}=3^{(11^x)} \\ 3^{1+3+5+7+...21}=3^{(11^x)} \\ Nr.~de~termeni = \frac{21-1}{2} +1 = \frac{20}{2} +1=10+1=11~termeni. \\ 3^{ \frac{11(21+1)}{2}}=3^{(11^x)} \\ \\ \frac{11(21+1)}{2}=11^x \\ \\ \frac{11\;\cdot\;22}{2}=11^x \\ 11\cdot11 = 11^x \\ 11^2=11^x \\ =\ \textgreater \ ~~x=\boxed{2}$