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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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You have entered [src] 
     /log(x)\
 lim |------|
x->0+\log(3)/
lim⁡x→0+(log⁡(x)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
02468-8-6-4-2-1010-1010
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(log⁡(x)log⁡(3))=−∞\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→0+(log⁡(x)log⁡(3))=−∞\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = -\infty
lim⁡x→∞(log⁡(x)log⁡(3))=∞\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}}\right) = \infty
More at x→oo
lim⁡x→1−(log⁡(x)log⁡(3))=0\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→1+(log⁡(x)log⁡(3))=0\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→−∞(log⁡(x)log⁡(3))=∞\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→0+(log⁡(x)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→0−(log⁡(x)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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