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log-2-x-logx-2-3-0-x-




Question Number 6111 by Kasih last updated on 14/Jun/16
log^2 x+logx^2 −3=0 , x=?
$${log}^{\mathrm{2}} {x}+{logx}^{\mathrm{2}} −\mathrm{3}=\mathrm{0}\:,\:{x}=? \\ $$
Answered by prakash jain last updated on 14/Jun/16
log x=u  u^2 +2u−3=0⇒(u+3)(u−1)=0  ⇒u=−3 or u=1  log x=−3 or log x=1  x=10^(−3)  or x=10^1
$$\mathrm{log}\:{x}={u} \\ $$$${u}^{\mathrm{2}} +\mathrm{2}{u}−\mathrm{3}=\mathrm{0}\Rightarrow\left({u}+\mathrm{3}\right)\left({u}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{u}=−\mathrm{3}\:{or}\:{u}=\mathrm{1} \\ $$$$\mathrm{log}\:{x}=−\mathrm{3}\:{or}\:\mathrm{log}\:{x}=\mathrm{1} \\ $$$${x}=\mathrm{10}^{−\mathrm{3}} \:{or}\:{x}=\mathrm{10}^{\mathrm{1}} \\ $$

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