SOLUTION: use log[2]3=(1.5850) and log[2]2=1 to approximate the value of the expression of log[2]9216

Question 752544: use log[2]3=(1.5850) and log[2]2=1 to approximate the value of the expression of log[2]9216
Found 2 solutions by Theo, tommyt3rd:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
9216 = 2^10 * 3^2
log(2,(9216) = log(2,(2^10 * 3^2)
log (2,(2^10 * 3^2) = log(2,2^10) + log(2,3^2)
log(2,2^10) + log(2,3^2) = 10 * log(2,2) + 2 * log(2,3)
10 * log(2,2) + 2 * log(2,3) = 10 * 1 + 2 * 1.5850 = 13.17.
you can use your calculator to confirm.
log(2,9216) = log(10,9216) / log(10,2) = LOG(9216) / LOG(2) = 13.l69925
that's pretty close (13.17 / 13.169925 = 1.000005695.

Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
We'll denote log base 2 by log2 and notice that 9216=2^10*3^2

Now we can write

:)
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