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log(x)/log(5)
Limit of the function/ log(x)/log(5)

Limit of the function log(x)/log(5)

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You have entered [src] 
     /log(x)\
 lim |------|
x->0+\log(5)/
lim⁡x→0+(log⁡(x)log⁡(5))\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) 
Limit(log(x)/log(5), 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
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(log⁡(x)log⁡(5))=−∞\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(log⁡(x)log⁡(5))=−∞\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = -\infty
lim⁡x→∞(log⁡(x)log⁡(5))=∞\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty
More at x→oo
lim⁡x→1−(log⁡(x)log⁡(5))=0\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0
More at x→1 from the left
lim⁡x→1+(log⁡(x)log⁡(5))=0\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = 0
More at x→1 from the right
lim⁡x→−∞(log⁡(x)log⁡(5))=∞\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) = \infty
More at x→-oo
One‐sided limits [src] 
     /log(x)\
 lim |------|
x->0+\log(5)/
lim⁡x→0+(log⁡(x)log⁡(5))\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) 
-oo
−∞-\infty 
= -5.50841094543338
     /log(x)\
 lim |------|
x->0-\log(5)/
lim⁡x→0−(log⁡(x)log⁡(5))\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right) 
-oo
−∞-\infty 
= (-5.50841094543338 + 1.95198126583117j)
= (-5.50841094543338 + 1.95198126583117j)
Numerical answer [src] 
-5.50841094543338
-5.50841094543338
The graph
Limit of the function log(x)/log(5)
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