Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 534: 8

$x = 496.5$

$\log (2x+7) = 3$ $\log_{10} (2x+7) = 3$ $10^{3} = 2x + 7$ $1000 = 2x + 7$ $1000 - 7 = 2x$ $993 = 2x$ $x = 496.5$ Check: $\log_{10} (2(496.5)+7) \overset{?}{=} 3$ $\log_{10} (993+7) \overset{?}{=} 3$ $\log_{10} (1000) \overset{?}{=} 3$ $\log_{10} (10^{3}) \overset{?}{=} 3$ $3 = 3$