Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 312: 83

$1$

Step 1. Rewrite the equation $\frac{ln(x+1)}{ln2}-\frac{ln(x)}{ln2^2}=1 \longrightarrow 2ln(x+1)=2ln2+ln(x) \longrightarrow (x+1)^2=4x \longrightarrow x^2-2x+1=0 \longrightarrow x=1$ Step 2. Check, $x=1$ fits the original equation.