Let a curve y=f(x) pass through (2,(_e2)^2) and have slope 2yx_ex.

Question

Let a curve $y=f(x)$ pass through $(2,(\log_e2)^2)$ and have slope $\dfrac{2y}{x\log_ex}$. Find $f(e)$.

Answer: 1

Accepted Answer

$$\frac{dy}{y}=\frac{2\,dx}{x\ln x} \implies \ln|y| = 2\ln|\ln x|+C.$$

Using the point: $C=0 \implies y=(\ln x)^2$. So $f(e)=1^2=1$.

Solutions · 1