SOLUTION: log2x(216)=x I know the answer is 3 (Calculator), but I don't know the steps required.

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Question 574529: log2x(216)=x
I know the answer is 3 (Calculator), but I don't know the steps required.
Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
That answer makes sense because
log%282x%2C216%29=x --> log%282x%2C6%5E3%29=x --> log%282x%2C%282%2A3%29%5E3%29=x
Maybe you were expected to graph and check. Maybe you would transform the equation like this:
log%282x%2C6%5E3%29=x --> 3log%282x%2C6%29=x --> 3log%283%2C6%29%2Flog%283%2C2x%29=x
At this point, you would realize that the graphs of the functions
y=3log%283%2C6%29%2Flog%283%2C2x%29 and y=x look like this, intersecting at just ore point that appears to be (3,3)
graph%28300%2C300%2C-1%2C5%2C-6%2C12%2C3log%283%2C6%29%2Flog%283%2C2x%29%2Cx%29
and making a further transformation, you would realize, and easily prove that x=3 is indeed the answer
3log%283%2C%282%2A3%29%29%2Flog%283%2C%282%2Ax%29%29=x --> 3%28log%283%2C2%29%2B1%29=x%28log%283%2C2%29%2Blog%283%2Cx%29%29