TAOCP 1.2.2 Exercise 16

By Eq.

taocpmathematicsalgorithmsvolume-1

Section 1.2.2: Numbers, Powers, and Logarithms

Exercise 16. [00] How can $\log_{10} x$ be expressed in terms of $\ln x$ and $\ln 10$?

Verified: yes
Solve time: 30s

By Eq. (15) we have $\ln x = \log_e x$. Applying the change-of-base formula (14) with $b = e$ and $c = 10$, we obtain

$\log_{10} x = \frac{\log_e x}{\log_e 10} = \frac{\ln x}{\ln 10}.$

This completes the solution. ∎