Question

${\int }_3^4\left(\frac{1}{x}\right)dx$ = $lo{g}_e\left(4/k\right)$. Find k

Answer 1

${\int }_3^4\frac{l}{x}dx$ (We know ${\int }_a^b\frac{1}{x}dx=\ln b-\ln a;=\ln \frac{b}{a}$)

$=\ln x{|}_3^4$

$=\ln 4-\ln 3$

$=\ln \frac{4}{3}$

Now, $\ln \frac{4}{3}=\ln \frac{4}{k}$

$\therefore k=3$