Question

determinati termenulnatural x stiindca 7 la puterea x +7 la puterea x+2=2450

Answer 1

${7}^{x} + {7}^{x + 2} = 2450 \\ {7}^{x} (1 + {7}^{2} ) = 2450 \\ 50 \times {7}^{x} = 2450 \\ {7}^{x} = 49$
De aici se deduce clar ca x = 2, dar evident ca se poate demonstra:
${7}^{x} = 49 \\ {7}^{x} = {7}^{2}$
Cand bazele sunt egale, comparam exponentii
=> x = 2

Answer 2

7^x + 7^(x+2) = 2 450

7^x + 7^x × 7^2 = 2 450

7^x × (1 + 7^2) = 2 450

7^x × 50 = 2 450

7^x = 2 450 : 50

7^x = 49

7^x = 7^2

x = 2
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