Question

Determinati numarul natural x care verifica egalitatile:
a) 2^x*2^5=2^13
b) 3^x*9^2=27^5
c) 5^x*25^3:125=625^2

Answer 1

$a).2^x*2^5=2^1^3 \\ 2^x*32=8192 \\ 2^x=8192:32 \\ 2^x=256 \\ 2^x=2^8 \\ x=8 \\ b).3^x*9^2=27^5 \\ 3^x*81=14348907 \\ 3^x=14348907:81 \\ 3^x=177147 \\ 3^x=3^1^1 \\ x=11$
$c).5^x*25^3:125=625^2 \\ 5^x*15625:125=390625 \\ 5^x=390625:15625*125 \\ 5^x=25*125 \\ 5^x=3125 \\ 5^x=5^5 \\ x=5$