Question

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

Answer 1

a) 3^x * 9^2=27^5
    3^x *(3^2)^2=(3^3)^5
    3^x * 3^4=3^15
    3^x=3^15:3^4
    3^x=3^11
    x=11

c) 5^x *25^3 : 125=625^2
    5^x *(5^2)^3 :5^3=(5^4)^2
    5^x * 5^6: 5^3=5^8
    5^x *5^6=5^8 *5^3
    5^x *5^6=5^11
    5^x =5^11 * 5^6
    5^x=5^15
    x=15