Question

The equation $\frac{{\log }_8\left(8/x^2\right)}{{\left({\log }_{8}x\right)}^2}=3$ has

• A. no integral solution
• B. one natural solution
• C. two real solutions
• D. one irrational solution

Answer 1

Answer: (B), (C)

$\frac{1-2y}{y^2}=3\left({\log }_{8}x=y\right)$
$3y^2+2y-1=0\Rightarrow 3y^2+3y-y-1=0\Rightarrow 3y(y+1)-1(y+1)$
${\log }_{8}x=y=1/3,-1\Rightarrow x=2,1/8$