Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 42

$x = 3.010$

$\log (x-3) = -2$ $\log_{10} (x-3) = -2$ $10^{-2} = x - 3$ $0.01 = x - 3$ $0.01 + 3 = x$ $x = 3.010$ Check: $\log_{10} (3.010-3) \overset{?}{=} -2$ $\log_{10} (0.01) \overset{?}{=} -2$ $\log_{10} (10^{-2}) \overset{?}{=} -2$ $-2\log_{10} (10) \overset{?}{=} -2$ $-2(1) \overset{?}{=} -2$ $-2 = -2$