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x-log-x-x-faind-x-




Question Number 136703 by mathlove last updated on 25/Mar/21
(√((√x)^(log x) ))=x       faind  x
$$\sqrt{\sqrt{{x}}\:^{\mathrm{log}\:{x}} }={x}\:\:\:\:\:\:\:{faind}\:\:{x} \\ $$
Commented by yutytfjh67ihd last updated on 25/Mar/21
Commented by MJS_new last updated on 25/Mar/21
some write log for log_e  and log_(10)  for log_(10)   some write log for log_(10)  and ln for log_e
$$\mathrm{some}\:\mathrm{write}\:\mathrm{log}\:\mathrm{for}\:\mathrm{log}_{\mathrm{e}} \:\mathrm{and}\:\mathrm{log}_{\mathrm{10}} \:\mathrm{for}\:\mathrm{log}_{\mathrm{10}} \\ $$$$\mathrm{some}\:\mathrm{write}\:\mathrm{log}\:\mathrm{for}\:\mathrm{log}_{\mathrm{10}} \:\mathrm{and}\:\mathrm{ln}\:\mathrm{for}\:\mathrm{log}_{\mathrm{e}} \\ $$
Answered by Olaf last updated on 25/Mar/21
(√((√x)^(log x) ))= x  x^((1/2)×(1/2)×logx) = x  x^((1/2)×(1/2)×logx) = x  x = 1 or (1/4)logx = 1  x = 1 or x = 10^4
$$\sqrt{\sqrt{{x}}\:^{\mathrm{log}\:{x}} }=\:{x} \\ $$$${x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{log}{x}} =\:{x} \\ $$$${x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{log}{x}} =\:{x} \\ $$$${x}\:=\:\mathrm{1}\:\mathrm{or}\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{log}{x}\:=\:\mathrm{1} \\ $$$${x}\:=\:\mathrm{1}\:\mathrm{or}\:{x}\:=\:\mathrm{10}^{\mathrm{4}} \\ $$
Answered by bramlexs22 last updated on 25/Mar/21
10^4 =x
$$\mathrm{10}^{\mathrm{4}} =\mathrm{x} \\ $$

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