Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 39

$r \approx3.389$

$\ln (r + 4) = 2$ $\log_e (r + 4) = 2$ $e^{2} = r + 4$ $r = e^{2} - 4$ $r \approx3.389$ Check: $\ln(( e^{2} - 4) + 4) \overset{?}{=} 2$ $\ln(e^{2} - 4 + 4) \overset{?}{=} 2$ $\ln(e^{2} ) \overset{?}{=} 2$ $2\log_e (e ) \overset{?}{=} 2$ $2(1) \overset{?}{=} 2$ $2= 2$