Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 37: 66

$\log_{2}(x^{2}+1)=\dfrac{\ln(x^{2}+1)}{\ln2}$

$\log_{2}(x^{2}+1)$ using base $e$ Apply the change of base formula, which is $\log_{b}x=\dfrac{\log_{a}x}{\log_{a}b}$ to express the given $\log$ using base $e$. In the formula, $x$ represents the argument of the $\log$, $b$ is the old base and $a$ is the new base. $\log_{2}(x^{2}+1)=\dfrac{\ln(x^{2}+1)}{\ln2}$