What is the limit as x approaches infinity of ln(7x+1)-ln(4x+1) ?

The limit as x approaches infinity of ln(7x+1)-ln(4x+1) is ln(7/4)

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limit as x approaches infinity of ln(7x+1)-ln(4x+1)

x \to \infty lim (ln (7 x + 1) - ln (4 x + 1))

ln (\frac{7}{4})

Decimal

0.55961 \dots

Solution steps

x \to \infty lim (ln (7 x + 1) - ln (4 x + 1))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (7 x + 1) - ln (4 x + 1) = ln (\frac{7 x + 1}{4 x + 1})

= x \to \infty lim (ln (\frac{7 x + 1}{4 x + 1}))

Apply the Limit Chain Rule:

ln (\frac{7}{4})

= ln (\frac{7}{4})

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What is the limit as x approaches infinity of ln(7x+1)-ln(4x+1) ?
The limit as x approaches infinity of ln(7x+1)-ln(4x+1) is ln(7/4)