omar wants to use a graph to solve the equation below. log₆x = log₂(x + 4) which system of equations should…

Explanation:

Step1: Recall the change - of - base formula

The change - of - base formula for logarithms is $\log_a b=\frac{\log_c b}{\log_c a}$, where $c$ can be any positive number other than 1. Usually, we use $c = 10$ (common logarithm) or $c=e$ (natural logarithm). For the left - hand side of the equation $\log_6x$, by the change - of - base formula, $\log_6x=\frac{\log x}{\log 6}$. For the right - hand side of the equation $\log_2(x + 4)$, by the change - of - base formula, $\log_2(x + 4)=\frac{\log(x + 4)}{\log 2}$.

Step2: Set up the system of equations

To solve the equation $\log_6x=\log_2(x + 4)$ using a graph, we set $y_1=\frac{\log x}{\log 6}$ and $y_2=\frac{\log(x + 4)}{\log 2}$. The $x$ - value of the intersection point of the graphs of $y_1$ and $y_2$ is the solution of the original equation.

Answer:

$y_1=\frac{\log x}{\log 6},y_2=\frac{\log(x + 4)}{\log 2}$