Question

Determină Nr natural x
Dau coroana​

Answer 1

Răspuns:

a)

${4}^{2} = ( {2}^{2} )^{2} = {2}^{2 \times 2} = {2}^{4}$

${8}^{3} = ( {2}^{3} )^{3} = {2}^{9}$

${2}^{x} = {2}^{4} \times {2}^{9} = > x = 4 + 9 = > x = 13$

b)

${9}^{4} = ( {3}^{2} )^{2} = {3}^{4}$

${27}^{5} = ( {3}^{3} )^{5} = {3}^{15}$

${3}^{x} = {3}^{4} \times {3}^{15} = > x = 19$

c)

${25}^{2} = ( {5}^{2} )^{2} = {5}^{4}$

${125}^{6} = ( {5}^{3} )^{6} = {5}^{18}$

${5}^{x} = {5}^{4} \times {5}^{18} = > x = 22$

d)

${4}^{3} = {2}^{6}$

${8}^{4} = {2}^{12}$

${16}^{5} = {2}^{20}$

$x = 6 + 12 + 20 = 38$

e)

${16}^{5} = {2}^{20}$

${4}^{x} = {2}^{2x}$

${2}^{2x} = {2}^{6} \times {2}^{20} = > 2x = 26 = > x = 13$

f)

${243}^{3} = ( {3}^{5} )^{3} = {3}^{15}$

${9}^{x} = {3}^{2x}$

${3}^{2x} = {3}^{11} \times {3}^{15} = > 2x = 26 = > x = 13$