Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 34

$\frac{1}{3}$

Step 1. Rewrite the equation as $log_{3}(x)+log_{3}(10^2)=log_{3}(x+1)+log_{3}(5^2) \longrightarrow log_{3}(100x)=log_{3}(25(x+1))$ Step 2. Thus $100x=25x+25\longrightarrow75x=25\longrightarrow x=\frac{1}{3}$. Step 3. Check answers, $x=\frac{1}{3}$ fits the original equation.