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Question Number 171847 by Mikenice last updated on 21/Jun/22

$$solve:$$$${log}_{x}10+{log}_{x^2}10=6$$

Commented by kaivan.ahmadi last updated on 21/Jun/22

$${log}_{x}10+\frac{1}{2}{log}_{x}10=6\Rightarrow \frac{3}{2}{log}_{x}10=6\Rightarrow$$$${log}_{x}10=4\Rightarrow x^4=10\Rightarrow x=\sqrt[4]{10}$$

Answered by cherokeesay last updated on 21/Jun/22

$$\iff \frac{ln10}{lnx}+\frac{ln10}{2lnx}=6(x>0)$$$$\frac{3ln10}{2lnx}=6\iff 10=x^4\iff$$$$x_1=\sqrt[4]{10},x_2=\sqrt[4]{10}i$$

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