Question

Solve for x the following equations :
$\frac{lo{g}_{2}x}{lo{g}_{4}2x}=\frac{lo{g}_{8}4x}{lo{g}_{8}8x}$

Answer 1

Put $lo{g}_{2}x$ = $t$
$\therefore lo{g}_{4}2x=\frac{1}{2}(lo{g}_{2}2+lo{g}_{2}x)=\frac{1}{2}(1+t)$
Hence the given equation is
$\frac{t}{1+t}=\frac{2(2+t)}{3(3+t)}$
or $t^2$ + 3t - 4 = 0 or t = 1, -4 = $lo{g}_{2}x$
$\therefore$ $x=2or$ $2^4$