Question

Determinați numărul natural x care verifică egalitatile
a)2^x*2^5=2^13
b)3^x*9^2=27^5
c)5x*25^3:125=625^2

Answer 1

$a).2^x \cdot 2^5=2^1^3 \\ 2^x=2^1^3:2^5 \\ 2^x=2^{13-5} \\ 2^x=2^8 \\ x=8$
$b).3^x \cdot 9^2=27^5 \\ 3^x=27^5:9^2 \\ 3^x=(3^3)^5:(3^2)^2 \\ 3^x=3^1^5:3^4 \\ 3^x=3^{15-4} \\ 3^x=3^1^1 \\ x=11$
$c).5^x \cdot 25^3:125=625^2 \\ 5^x:125=625^2:25^3 \\ 5^x:125=(25^2)^2:25^3 \\ 5^x:125=25^4:25^3 \\ 5^x:125=25^{4-3} \\ 5^x:125=25 \\ 5^x=25 \cdot 125 \\ 5^x=3125 \\ 5^x=5^5 \\ x=5$