please help me with limits for my exam tommrow

[elite_boy]

1) Lim x->0 log x -log a(x-a)
2) Lim x->a x^a -a^a(a^x -a^a)
3) lim x->infinity x/2^x

 

[Deleted member 4993]

1) Lim x->0 log x -log a(x-a)
2) Lim x->a x^a -a^a(a^x -a^a)
3) lim x->infinity x/2^x

Have you learned about L'Hospital's theorem?

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[HallsofIvy]

1) Lim x->0 log x -log a(x-a)

before you use "L'Hopital's rule" for this one use the "laws of logarithms: \(\displaystyle log(x)- log(a(x- a))= \log(\frac{x}{a(x- a)})\) and the fact that logarithm is continuous where ever it is defined: \(\displaystyle \lim_{x\to 0} log(x)- log(a(x- a))= log(\lim_{x\to 0}\frac{x}{a(x- a)})\).

2) Lim x->a x^a -a^a(a^x -a^a)
3) lim x->infinity x/2^x