The graphs of the equations log6(x) = 1 and log2(2x) = 2 intersect at a specific point. To find this point, we need to solve both equations separately.
For the equation log6(x) = 1, this means that the value of x must equal 61 = 6. Therefore, the first equation gives us the point (6, 1).
For the second equation log2(2x) = 2, we can rewrite it as 2x = 22. Simplifying this, we find that 2x = 4 or x = 2. Thus, the second equation gives us the point (2, 2).
To summarize, the two graphs represent different logarithmic functions, and they will not intersect at the same x-value. Therefore, neither equation will have a common solution when graphed together.
In conclusion, since the two equations do not give the same x-value, the graph of this equation does not show a common intersection point that satisfies both equations. Each equation will produce distinct points on the graph.