Question

Solve log3(x + 1) = log6(5 – x) by graphing.

What equations should be graphed?
mr001-1.jpg
mr001-2.jpg
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Graph the system. Use the graph to approximate the solution of the equation.

Answer 1

Graph the two functions
- y = log_3(x + 1)
- y = log_6(5 − x)

(Their domains are −1 < x < 5.)

The intersection of these two graphs is the solution of log_3(x+1) = log_6(5−x). Using a calculator/graph, the curves intersect at about
x ≈ 1.249 (y ≈ 0.738).

(You can also solve numerically by setting ln(x+1)/ln3 = ln(5−x)/ln6 and using a root finder on that equation.)