A) \[2\,\,\log \,a\]
B) \[1/\,\,\log \,a\]
C) \[\log \,a\]
D) \[{{a}^{{{2}_{{{x}_{1}}}}}}\log \,a\]
Correct Answer: B
Solution :
Given curve is \[y={{a}^{x}}\] \[\therefore \] \[\frac{dy}{dx}={{a}^{x}}\,\log \,a\] Now, length of sub tangent at any point \[({{x}_{1}},{{y}_{1}})\]is \[=\frac{y}{dy/dx}=\frac{{{a}^{{{x}_{1}}}}}{{{a}^{{{x}_{1}}}}\,\log \,a}\] \[=\frac{1}{\log \,a}\]
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