Răspuns:
a)
[tex] {4}^{2} = ( {2}^{2} )^{2} = {2}^{2 \times 2} = {2}^{4} [/tex]
[tex] {8}^{3} = ( {2}^{3} )^{3} = {2}^{9} [/tex]
[tex] {2}^{x} = {2}^{4} \times {2}^{9} = > x = 4 + 9 = > x = 13[/tex]
b)
[tex] {9}^{4} = ( {3}^{2} )^{2} = {3}^{4} [/tex]
[tex] {27}^{5} = ( {3}^{3} )^{5} = {3}^{15} [/tex]
[tex] {3}^{x} = {3}^{4} \times {3}^{15} = > x = 19[/tex]
c)
[tex] {25}^{2} = ( {5}^{2} )^{2} = {5}^{4} [/tex]
[tex] {125}^{6} = ( {5}^{3} )^{6} = {5}^{18} [/tex]
[tex] {5}^{x} = {5}^{4} \times {5}^{18} = > x = 22[/tex]
d)
[tex] {4}^{3} = {2}^{6} [/tex]
[tex] {8}^{4} = {2}^{12} [/tex]
[tex] {16}^{5} = {2}^{20} [/tex]
[tex]x = 6 + 12 + 20 = 38[/tex]
e)
[tex] {16}^{5} = {2}^{20} [/tex]
[tex] {4}^{x} = {2}^{2x} [/tex]
[tex] {2}^{2x} = {2}^{6} \times {2}^{20} = > 2x = 26 = > x = 13[/tex]
f)
[tex] {243}^{3} = ( {3}^{5} )^{3} = {3}^{15} [/tex]
[tex] {9}^{x} = {3}^{2x} [/tex]
[tex] {3}^{2x} = {3}^{11} \times {3}^{15} = > 2x = 26 = > x = 13[/tex]
