Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 6

$4$

The domain of the variable requires that $x+6>0$, which means that $x>-6$. Recall: $y=\log_a{x} \implies a^y=x$ Thus, $\log(x+6)= 1 \\ \implies 10^1=x+6\\ \implies 10=x+6$ Solve the equation to obtain: \begin{align*} 10-6&=x\\ 4&=x \end{align*}