Question

Determinati x din egalitatea : 4^5 inmultit cu 2^14 inmultit cu x + 8^9 = 4^14

Answer 1

4⁵·2¹⁴·x+8⁹=4¹⁴
[2²]⁵·2¹⁴·x+[2³]⁹=[2²]14
2¹⁰·2¹⁴·x+2²⁷=2²⁸
2¹⁰⁺¹⁴·x+2²⁷=2²⁸
2²⁴·x=2²⁷=2²⁸
2²⁴·x=2²⁸-2²⁷
2²⁴·x=2²⁷[2-1]
2²⁴·x=2²⁷⇒x=2³⇒x=8∈N;