Question

Se log8x + log82x = 5/3, o valor de x é?

Answer 1

Olá
Resoluçao

$log_{8} x+ log_{8} 2x= \frac{5}{3} \\ \frac{ log_{2}x }{ log_{2}8 }+ \frac{ log_{2}2x }{ log_{2}8 } = \frac{5}{3} \\ \frac{ log_{2} x}{ log_{2} 2^{3} }+ \frac{ log_{2}2x }{ log_{2} 2^{8} } = \frac{5}{3} \\ \\ \frac{ log_{2}x }{3 log_{2}2 } + \frac{ log_{2}2x}{3 log_{2}2 } = \frac{5}{3} \\ \frac{ log_{2}x }{3} + \frac{ log_{2} 2x}{3} = \frac{5}{3} \\ log_{2} x+ log_{2} 2x=5 \\ log_{2}.2 x^{2}=5 \\ 2^{5} =2 x^{2} \\ x^{2} = 2^{4} \\ x= \sqrt{ 2^{4} } \\ x= 2^{2} \\ x=4$

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