Key Skill - Determine an unknown power.

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"Determine an unknown power."
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Is there a formulaic way to solve this? For example, if I know that my base is 2, and I'm solving for some unknown power which it is raised to in order to give me a final answer of, say, 16384, is there an easy way to know that my unknown power should be 14? In the three examples you offer, it's easy to see that the number should be -3 since we're dealing with small numbers, but how do you approach this type of problem when the solution isn't as clear?

For example 2^x=16384 -> in this case x should be 14, but do I actually have to trial and error my way up to 14? Is there an easier way? Thank you

goosemunky
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These examples are too simple. What about for more complicated numbers??

thesuperiorman