Just take a logarithm to the base of 5 from both sides to cancel the base and get the `x` back:

log_5(5^x) = log_5(390211)

x = log_5(390211)

So now the problem is another question (a bit simpler):

What power of 5 gives us 390211?

5^7 is too few: 78125.

5^8 is too much: 390625, but very close. If you try something between, you’ll get closer and closer approximation. It will be something around 7.999341135…

So the answer is: 5^7.999341135… = 390211 ]]>

Furthermore, since 390211 isn’t even an integer multiple of five, much less an integer power of five, we can’t use elementary methods such as prime factorization to find x.

That leaves one viable path: logarithms.

I’ll leave the rest to your own devices….

]]>5 to the power of x = 390211

pls. send your answer thanks

]]>A little while back, several of my fellow math-and-science bloggers and I got into a discussion of a particularly hare-brained way to reform math education, and I mentioned that nobody in my generation seems to have learned how to take square roots by …

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