tenisha solved the equation below by graphing a system of equations. $log_3{5x}=log_5{(2x + 8)}$ which point…

Explanation:

Step1: Recall the property of logarithmic - equation solutions

The solution of the equation (\log_{3}(5x)=\log_{5}(2x + 8)) is the (x) - value for which the two functions (y_1=\log_{3}(5x)) and (y_2=\log_{5}(2x + 8)) have the same (y) - value. We can check each point ((x,y)) by substituting (x) into both functions and seeing if the (y) - values are approximately equal.

Step2: Substitute (x = 0.9) into (y_1=\log_{3}(5x))

[y_1=\log_{3}(5\times0.9)=\log_{3}(4.5)=\frac{\ln(4.5)}{\ln(3)}\approx1.465] [y_2=\log_{5}(2\times0.9 + 8)=\log_{5}(9.8)=\frac{\ln(9.8)}{\ln(5)}\approx1.464]

Step3: Substitute (x = 1.0) into (y_1=\log_{3}(5x))

[y_1=\log_{3}(5\times1)=\log_{3}(5)=\frac{\ln(5)}{\ln(3)}\approx1.465] [y_2=\log_{5}(2\times1+8)=\log_{5}(10)=\frac{\ln(10)}{\ln(5)}\approx1.431]

Step4: Substitute (x = 2.3) into (y_1=\log_{3}(5x))

[y_1=\log_{3}(5\times2.3)=\log_{3}(11.5)=\frac{\ln(11.5)}{\ln(3)}\approx2.27] [y_2=\log_{5}(2\times2.3 + 8)=\log_{5}(12.6)=\frac{\ln(12.6)}{\ln(5)}\approx1.54]

Step5: Substitute (x = 2.7) into (y_1=\log_{3}(5x))

[y_1=\log_{3}(5\times2.7)=\log_{3}(13.5)=\frac{\ln(13.5)}{\ln(3)}\approx2.46] [y_2=\log_{5}(2\times2.7+8)=\log_{5}(13.4)=\frac{\ln(13.4)}{\ln(5)}\approx1.58]

Answer:

((0.9,0.8))