Question

5. Determinați numărul natural x: 2^x-3 =(2^10)^3:4^9​

Answer 1

Răspuns:

x=15

Explicație pas cu pas:

${2}^{x - 3} = \frac{ { ({2}^{10}) }^{3} }{ {4}^{9} } \\ {2}^{x - 3} = \frac{ {2}^{10 \times 3} }{ {( {2}^{2}) }^{9} } \\ {2}^{x - 3} = \frac{ {2}^{30} }{ {2}^{2 \times 9} } \\ {2}^{x - 3} = \frac{ {2}^{30} }{ {2}^{18} } \\ \\ {2}^{x - 3} = {2}^{30 - 18} \\ {2}^{x - 3} = {2}^{12} = > x - 3 = 12 \\ x = 3 + 12 \\ x = 15$