Question

Which graph shows the solution to the equation below?

log Subscript 3 Baseline (x + 3) = log Subscript 0.3 (x minus 1)
On a coordinate plane, 2 curves intersect at (1, 1). One curve curves up and to the right from quadrant 3 into quadrant 1. The other curve curves down from quadrant 1 into quadrant 4.
On a coordinate plane, 2 identical curves are shown. One curve starts at y = negative 3, and the other curve starts at y = 1.
On a coordinate plane, a curve and a line are shown.
On a coordinate plane, a curve and a cubic function are shown.

Answer 1

Choose the first graph.

Reason: the equation is y = log_3(x+3) and y = log_{0.3}(x-1). y = log_3(x+3) is increasing with vertical asymptote x = −3 (rising from QIII through QII into QI). y = log_{0.3}(x-1) is decreasing with vertical asymptote x = 1 (coming down from QI into QIV). Their intersection lies in quadrant I (x > 1), so the picture showing one curve curving up from QIII into QI and the other curving down from QI into QIV is the correct one.