Question

9 pontos 

 

Qual é o valor da incógnita x na igualdade log na base 9 de raiz quadrada de 108 = x

Answer 1

$x=log _{9} ^{ \sqrt{108} } = \frac{log \sqrt{108} }{log9} = \frac{log108 \frac{1}{2} }{log3^2} = \frac{ \frac{1}{2}log2^2.3^3 }{2.log3} = \\ \\ \frac{ \frac{1}{2}.(2.log2+3log3) }{2.log3}= \frac{2.log2+3.log3}{4.log3}= \\ \\ \frac{2.0,3010 +3.0,4771}{4.0,4771} = \frac{2,0333}{1,9084} =1,0654$