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?
(0.9, 0.8)
(1.0, 1.4)
(2.3, 1.1)
(2.7, 13.3)

Explanation:

Step1: Define the two functions

Let $f(x) = \log_{3}(5x)$ and $g(x) = \log_{5}(2x+8)$. We need to find $x$ where $f(x)=g(x)$, then verify the corresponding $y$-value.

Step2: Test option (0.9, 0.8)

Calculate $f(0.9)=\log_{3}(5*0.9)=\log_{3}(4.5)\approx1.356$, which does not equal 0.8. Eliminate this option.

Step3: Test option (1.0, 1.4)

Calculate $f(1.0)=\log_{3}(5*1)=\log_{3}(5)\approx1.465$, and $g(1.0)=\log_{5}(2*1+8)=\log_{5}(10)\approx1.431$. Both values are approximately 1.4, matching the given $y$-value.

Step4: Verify remaining options (optional)

For (2.3, 1.1): $f(2.3)=\log_{3}(11.5)\approx2.18$, not 1.1. For (2.7, 13.3): $f(2.7)=\log_{3}(13.5)\approx2.43$, not 13.3. These are invalid.

Answer:

B. (1.0, 1.4)