Write the logarithm $\log_5120$ in terms of the natural logarithm. Evaluate the value of the new logarithm with the help of a calculator. Write your answer using four decimal places.

Rewrite the expression $\ln\left|x\right|$ using base 8.

Express the expression $k^{\frac{3}{\ln k}}$ in terms of the natural base e, for $k > 0$ and $k ≠ 1$.

Solve the equation $100=20e^{3k}$ for $k$.