What is the limit as x approaches infinity of ln(9x)-ln(x+7) ?

The limit as x approaches infinity of ln(9x)-ln(x+7) is 2ln(3)

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limit as x approaches infinity of ln(9x)-ln(x+7)

x \to \infty lim (ln (9 x) - ln (x + 7))

2 ln (3)

Decimal

2.19722 \dots

Solution steps

x \to \infty lim (ln (9 x) - ln (x + 7))

Apply log rule:

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

ln (9 x) - ln (x + 7) = ln (\frac{9 x}{x + 7})

= x \to \infty lim (ln (\frac{9 x}{x + 7}))

Apply the Limit Chain Rule:

2 ln (3)

= 2 ln (3)

What is the limit as x approaches infinity of ln(9x)-ln(x+7) ?
The limit as x approaches infinity of ln(9x)-ln(x+7) is 2ln(3)