1976 AMC 12 Question 20 - thichhoctoan.com

Question 20

Let $a,$ $b$ and $x$ be positive real numbers distinct from one. Then $$
\begin{aligned} 4(\log_a x)^2&+3(\log_b x)^2\\ &=8(\log_a x)(\log_b x) \end{aligned}
$$

for all values of $a,$ $b$ and $x$
if and only if $a=b^2$
if and only if $b=a^2$
if and only if $x=ab$
none of these