Reciprocal of Logarithm/Examples/Logarithm Base 10 of 2

Example of Reciprocal of Logarithm

The reciprocal of $\log_{10} 2$ is $\log_2 10$.

Proof

From Reciprocal of Logarithm:

$\dfrac 1 {\log_x y} = \log_y x$

Let $x = 10, y = 2$:

Then: $\dfrac 1 {\log_{10} 2} = \log_2 10$

$\blacksquare$

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: Exercise $20$