1976 AHSME Problem 20

Let a,~b, and x be positive real numbers distinct from one. Then 4(\log_ax)^2+3(\log_bx)^2=8(\log_ax)(\log_bx)

\begin{array}{l} \textbf{(A) }\text{for all values of }a,~b,\text{ and }x\qquad\\ \textbf{(B) }\text{if and only if }a=b^2\qquad\\ \textbf{(C) }\text{if and only if }b=a^2\qquad\\ \textbf{(D) }\text{if and only if }x=ab\qquad\\ \textbf{(E) }\text{for none of these} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.