How do you find the Limit of $ln (x)/ln (3x)$ as x approaches infinity?

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Answer 1 · 2016-08-15T19:51:26

$1$

$lim_(x to oo) ln (x)/ln (3x)$

$lim_(x to oo) ln (x)/(ln 3 + ln x )$

$lim_(x to oo) 1/(ln 3/ (ln x ) + 1 )$

$(lim_(x to oo) 1)/(lim_(x to oo) ln 3/ (ln x ) + 1 )$

$= 1/1 = 1$ as $lim_(x to oo) ln (x) = oo$

How do you find the Limit of ln (x)/ln (3x) ln (x)/ln (3x) as x approaches infinity?