Question

log 2 ( 3x ² - 1 ) = 4​

Answer 1

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$\sf \ell og_2(3x^2-1)=4\\\sf 3x^2-1=2^4\\\sf 3x^2-1=16\\\sf 3x^2=16+1\\\sf3x^2=17\\\sf x^2=\dfrac{17}{3}\\\sf x=\sqrt{\dfrac{17}{3}}\\\sf x=\dfrac{\sqrt{17}}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{\sqrt{51}}{3}\checkmark}}}}$

Answer 2

$\underbrace{ \sf{veja \: abaixo}} : \\ \\ \sf{log_{2}(3 {x}^{2} - 1 ) = 4} \\ \\ \sf{3 {x}^{2} - 1 = {2}^{4} } \\ \\ \sf{3 {x}^{2} - 1 = 16} \\ \\ \sf{3 {x}^{2} = 16 + 1} \\ \\ \sf{3 {x}^{2} = 17} \\ \\ \sf{{x}^{2} = \frac{17}{3} } \\ \\ \sf{x = \sqrt{ \dfrac{17}{3} } } \\ \\ \sf{x = } \begin{bmatrix} \: \sf{ \dfrac{ \sqrt{17} }{ \sqrt{3} } \: \: \cdot \: \: \dfrac{ \sqrt{3} }{ \sqrt{3} } } \end{bmatrix} \\ \\ \red{ \boxed{ \boxed{ \maltese \: \sf{x = \sqrt{ \dfrac{51}{3} } }}}}$

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