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(1-log(7*x))^(7*x)
Limit of the function/ (1-log(7*x))^(7*x)

Limit of the function (1-log(7*x))^(7*x)

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                   7*x
 lim (1 - log(7*x))   
x->0+
lim⁡x→0+(1−log⁡(7x))7x\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} 
Limit((1 - log(7*x))^(7*x), 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
02468-8-6-4-2-1010010e35
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(1−log⁡(7x))7x=1\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1
More at x→0 from the left
lim⁡x→0+(1−log⁡(7x))7x=1\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1
lim⁡x→∞(1−log⁡(7x))7x=0\lim_{x \to \infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0
More at x→oo
lim⁡x→1−(1−log⁡(7x))7x=−21log⁡(7)5−35log⁡(7)3−log⁡(7)7−7log⁡(7)+1+21log⁡(7)2+7log⁡(7)6+35log⁡(7)4\lim_{x \to 1^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}
More at x→1 from the left
lim⁡x→1+(1−log⁡(7x))7x=−21log⁡(7)5−35log⁡(7)3−log⁡(7)7−7log⁡(7)+1+21log⁡(7)2+7log⁡(7)6+35log⁡(7)4\lim_{x \to 1^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}
More at x→1 from the right
lim⁡x→−∞(1−log⁡(7x))7x=0\lim_{x \to -\infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0
More at x→-oo
One‐sided limits [src] 
                   7*x
 lim (1 - log(7*x))   
x->0+
lim⁡x→0+(1−log⁡(7x))7x\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} 
1
11 
= (1.00335674408759 - 9.38301555323147e-6j)
                   7*x
 lim (1 - log(7*x))   
x->0-
lim⁡x→0−(1−log⁡(7x))7x\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} 
1
11 
= (0.996595785860645 + 0.000625569892627682j)
= (0.996595785860645 + 0.000625569892627682j)
Numerical answer [src] 
(1.00335674408759 - 9.38301555323147e-6j)
(1.00335674408759 - 9.38301555323147e-6j)
The graph
Limit of the function (1-log(7*x))^(7*x)
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