Question

The length of the subtangent at any point $(x_1,y_1)$ on the curve $y=5^x$ is

• A. $5^{x_1}$
• B. $y_1{.5}^{x_1}$
• C. ${\log }_{e}5$
• D. $\frac{1}{{\log }_{e}5}$

Answer 1

Answer: (D)

$\frac{1}{{\log }_{e}5}$

Given, $y=5^x$

$\Rightarrow y^{\prime }=5^x\ln 5$

Hence length of subtangent $=\frac{y}{y^{\prime }}=\frac{5^x}{5^x\ln 5}=\frac{1}{{\log }_{e}5}$