Question

Which system of equations could be graphed to solve the equation below?

log Subscript 0.5 Baseline x = log Subscript 3 Baseline 2 + x
y 1 = StartFraction log 0.5 Over x EndFraction , y 2 = StartFraction log 3 Over 2 + x EndFraction
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 + x Over log 3 EndFraction
y 1 = StartFraction log 0.5 Over log 3 EndFraction, y 2 = StartFraction log x Over log 2 + x EndFraction
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 Over log 3 EndFraction + x

Answer 1

Write each logarithm with a common base (change-of-base): log_{0.5} x = (log x)/(log 0.5) and log_{3}(2+x) = (log(2+x))/(log 3).

So graph the system
y1 = (log x)/(log 0.5), y2 = (log(2+x))/(log 3),

which is the second choice.