Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 61

$x \approx 3.333 \times 10^{-4}$

$2 \log(3x) + 8 = 2$ $2 \log 3x = 2 - 8$ $2 \log 3x = -6$ $\log 3x = -3$ $10^{-3} = 3x$ $0.001 = 3x$ $x = \frac{0.001}{3}$ $x \approx 3.333 \times 10^{-4}$ Check: $2 \log(3x) + 8 = 2$ $2 \log(3( \frac{0.001}{3})) + 8 \overset{?}{=} 2$ $2 \log(0.001) + 8 \overset{?}{=} 2$ $2(-3) + 8 \overset{?}{=} 2$ $-6 + 8 \overset{?}{=} 2$ $2 = 2$