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Question-70198




Question Number 70198 by smartsmith459@gmail.com last updated on 01/Oct/19
Answered by MJS last updated on 01/Oct/19
x=a^(√(log_a  b))   ln x =(√((ln b)/(ln a)))ln a =(√(ln a ×ln b))  ⇒ 5^(√(log_5  7)) −7^(√(log_7  5)) =0
$${x}={a}^{\sqrt{\mathrm{log}_{{a}} \:{b}}} \\ $$$$\mathrm{ln}\:{x}\:=\sqrt{\frac{\mathrm{ln}\:{b}}{\mathrm{ln}\:{a}}}\mathrm{ln}\:{a}\:=\sqrt{\mathrm{ln}\:{a}\:×\mathrm{ln}\:{b}} \\ $$$$\Rightarrow\:\mathrm{5}^{\sqrt{\mathrm{log}_{\mathrm{5}} \:\mathrm{7}}} −\mathrm{7}^{\sqrt{\mathrm{log}_{\mathrm{7}} \:\mathrm{5}}} =\mathrm{0} \\ $$

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