Math CentralQuandaries & Queries


Question from Ericha, a student:

How do I express 1,679,616 in exponential form as a power of 6 using a calculator?

We have two responses for you

Hi Ericha. Use logarithms.

In general, if I have the base 10 number N and I want to express it as
a power of B, then let p = the unknown power so:

N = Bp
log(N) = log(Bp)
log(N) = p log(B)
p = log(N) / log(B).

So in your case,

p = log(1679616) / log(6)

Stephen La Rocque.


Hi Ericha,

My first thought was "I wonder if 1,679,616 is an integer power of 6?" I know that 62 = 36 so I used my calculator to find 362 = 1296 and then I divided 1,679,616 by 1296.

Steve's response is the "correct" method. Mine only worked because 1,679,616 is an integer power of 6.


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