Question

Fuvest o número x 1 tal que log x 2 = log 4X​

Answer 1

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$\sf{\ell og_x2=\ell og_4x}\\\sf{\dfrac{\ell og_42}{\ell og_4x}=\ell og_4x}\\\sf{(\ell og_4x)^2=\ell og_42}\\\sf{(\ell og_4x)^2-\ell og_42=0}\\\sf fac_{\!\!,}a~\ell og_4x=y\\\sf{y^2-\ell og_42=0}\\\sf y^2-\ell og_{2^2}2=0\\\sf{y^2-\frac{1}{2}\ell og_22=0}\\\sf{y^2-\dfrac{1}{2}=0}\\\sf y^2=\dfrac{1}{2}$

$\sf y=\sqrt{\dfrac{1}{2}}\\\sf \ell og_4x=\sqrt{\dfrac{1}{2}}\\\sf{x=4^{\sqrt{\frac{1}{2}}}}\\\sf{x=2^{2\sqrt{\frac{1}{2}}}}\\\sf{x=2^{\sqrt{2^2\cdot\frac{1}{2}}}}\\\sf{x=2^{\sqrt{2}}}$