Question

Exercitiul 9 pls help.

Answer 1

$b) 5^{9} *5^{41} * 5^{59}*5= 5^{x} \\5^{9+41+59+1)} = 5^{x} \\x=9+41+59+1 \\x=110 \\d) 3 ^{2538} : 3^{1999} :( 3 ^{5} )^{100} *9=3^{x} \\ 3 ^{2538-1999} :3^{5*100}* 3^{2} = 3^{x} \\ 3^{539} : 3^{500} * 3^{2} =3^{x} \\ 3^{539-500} * 3^{2} =3^{x} \\ 3 ^{39} * 3^{2} =3^{x} \\ 3^{39+2} =3^{x} \\ 3^{41} =3^{x} \\ x=41 \\ f)( 14^{123}) ^{43} : (14^{23} ) ^{3} : 7^{17} = 2^{x} \\ 14^{2*43} : 14^{23*3} : 7^{17}= 2^{x} \\ 14^{86-69} :7^{17}= 2^{x} \\( 2*7) ^{17}: 7^{17} = 2^{x} \\ 2^{17} = 2^{x} \\ x=17$