# Evaluate the limit using L'Hospital's rule if necessary lim as x approaches infinity of (15x)((ln(7)+1)/(ln(12x)+1))

You need to substitute oo for x in limit such that:

`lim_(x-gtoo) (15x)(ln(7)+1)/(ln(12x)+1) = oo/oo`

You should use l'Hospital's theorem such that:

`lim_(x-gtoo) ((15x(ln(7)+1))')/((ln(12x)+1)') = lim_(x-gtoo) (15(ln(7)+1))/(1/x)`

`lim_(x-gtoo) (15(ln(7)+1))/(1/x) = (15(ln(7)+1))/(1/oo) = oo`

Hence, evaluating the limit to the function using l'Hospital's theorem yields `lim_(x-gtoo) (15x(ln(7)+1)/(ln(12x)+1)) = oo.`

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You need to substitute oo for x in limit such that:

`lim_(x-gtoo) (15x)(ln(7)+1)/(ln(12x)+1) = oo/oo`

You should use l'Hospital's theorem such that:

`lim_(x-gtoo) ((15x(ln(7)+1))')/((ln(12x)+1)') = lim_(x-gtoo) (15(ln(7)+1))/(1/x)`

`lim_(x-gtoo) (15(ln(7)+1))/(1/x) = (15(ln(7)+1))/(1/oo) = oo`

Hence, evaluating the limit to the function using l'Hospital's theorem yields `lim_(x-gtoo) (15x(ln(7)+1)/(ln(12x)+1)) = oo.`

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