Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 35

$h = -8192$

$\log_4 (-2h) + 40 = 47$ $\log_4 (-2h) = 47 - 40$ $\log_4 (-2h) = 7$ $4^{7} = -2h$ $16384 = -2h$ $h = -8192$ Check: $\log_4 (-2(-8192)) + 40 \overset{?}{=} 47$ $\log_4 (16384) + 40 \overset{?}{=} 47$ $\log_4 (4^{7}) + 40 \overset{?}{=} 47$ $7\log_4 (4) + 40 \overset{?}{=} 47$ $7(1) + 40 \overset{?}{=} 47$ $7+ 40 \overset{?}{=} 47$ $47 = 47$