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log(x)/log(3)
Limit of the function/ log(x)/log(3)

Limit of the function log(x)/log(3)

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The solution

You have entered [src] 
     /log(x)\
 lim |------|
x->0+\log(3)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right)$$ 
Limit(log(x)/log(3), x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = \infty$$
More at x→-oo
Rapid solution [src] 
-oo
$$-\infty$$
Expand and simplify
One‐sided limits [src] 
     /log(x)\
 lim |------|
x->0+\log(3)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right)$$ 
-oo
$$-\infty$$ 
= -8.06685102955841
     /log(x)\
 lim |------|
x->0-\log(3)/
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right)$$ 
-oo
$$-\infty$$ 
= (-8.06685102955841 + 2.85960086738013j)
= (-8.06685102955841 + 2.85960086738013j)
Numerical answer [src] 
-8.06685102955841
-8.06685102955841
The graph
Limit of the function log(x)/log(3)
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