1978 AMC 12 Question 21
AMC12 · 1978 AMC 12
For all positive numbers $x$ distinct from $1,$ $$
\frac1{\log_3x}+\frac1{\log_4x}+\frac1{\log_5x}
$$ equals
$\frac1{\log_{60}x}$
$\frac1{\log_x60}$
$\frac1{(\log_3x)(\log_4x)(\log_5x)}$
$\frac{12}{(\log_3x)+(\log_4x)+(\log_5x)}$
$\frac{\log_2x}{(\log_3x)(\log_5x)}$
${}+\frac{\log_3x}{(\log_2x)(\log_5x)}$
${}+\frac{\log_5x}{(\log_2x)(\log_3x)}$