Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 33

$x = 50$

$\log (2x) + 5 = 7$ $\log 2x = 7 -5$ $\log 2x = 2$ $10^{2} = 2x$ $100 = 2x$ $x = 50$ Check: $\log (2(50)) + 5 \overset{?}{=} 7$ $\log (100) + 5 \overset{?}{=} 7$ $\log_{10} (10^{2}) + 5 \overset{?}{=} 7$ $2\log_{10} (10) + 5 \overset{?}{=} 7$ $2 + 5 \overset{?}{=} 7$ $7 = 7$