Question

tenisha solved the equation below by graphing a system of equations.\\(\log_{3}5x = \log_{5}(2x + 8)\\)\
which point approximates the solution for tenishas system of equations?\
\\(\circ\\) \\((0.9, 0.8)\\)\
\\(\circ\\) \\((1.0, 1.4)\\)\
\\(\circ\\) \\((2.3, 1.1)\\)\
\\(\circ\\) \\((2.7, 13.3)\\)

Explanation:

Step1: Define the system

To solve \(\log_{3}5x=\log_{5}(2x + 8)\) by graphing, we consider the system of equations \(y=\log_{3}5x\) and \(y=\log_{5}(2x + 8)\). The solution is the point \((x,y)\) where these two graphs intersect, meaning \(x\) and \(y\) satisfy both equations.

Step2: Test each option

• For \((0.9,0.8)\):
• Calculate \(y=\log_{3}(5\times0.9)=\log_{3}4.5\approx1.365\), which is not close to \(0.8\). So this is not a solution.
• For \((1.0,1.4)\):
• Calculate \(y=\log_{3}(5\times1.0)=\log_{3}5\approx1.465\), and \(y=\log_{5}(2\times1.0 + 8)=\log_{5}10\approx1.431\). Both values are close to \(1.4\), so this is a good approximation.
• For \((2.3,1.1)\):
• Calculate \(y=\log_{3}(5\times2.3)=\log_{3}11.5\approx2.19\), which is not close to \(1.1\). So this is not a solution.
• For \((2.7,13.3)\):
• Calculate \(y=\log_{3}(5\times2.7)=\log_{3}13.5\approx2.405\), which is not close to \(13.3\). So this is not a solution.

Answer:

B. (1.0, 1.4)