Question

Solve log2x = log12x by graphing.

What equations should be graphed?
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mr001-2.jpg
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Graph the system. Use the graph to solve the equation.

x =

Answer 1

Graph the two functions
y = log_2 x and y = log_{12} x.

They intersect where log_2 x = log_{12} x. Let that common value be y, so x = 2^y = 12^y. Then 2^y = 12^y ⇒ (12/2)^y = 6^y = 1 ⇒ y = 0, hence x = 2^0 = 1.

So the graphs meet at (1,0) and the solution is x = 1.