Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 84

$1$

1. $log_2(x+1)-log_4(x)=1 \Longrightarrow \frac{log(x+1)}{log2}-\frac{log(x)}{log4}=1 \Longrightarrow \frac{log(x+1)}{log2}-\frac{log(x)}{2log2}=1\Longrightarrow 2log(x+1)-log(x)=2log2 \Longrightarrow (x+1)^2=4x \Longrightarrow x^2-2x+1=0 \Longrightarrow x=1 $ 2. Check, $x=1$ fit.