A Significantly Large Number
What is the magnitude of the following number: ?
Note: The number 45 has a magnitude of 1 (10), the number 53,572,964 has a magnitude of 7 (10,000,000), and the number has a magnitude of 76.
The answer is 1975.
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1 solution
We know that 3 ( 2 3 ) is equal to 6561. That means that we want to know the magnitude of 2 6 5 6 1 .
We can make a general equation for the magnitude of a number when raised to a base of 2. This will allow us to determine the magnitude depending on what two is raised to.
2 x = 1 0 y
l o g 1 0 ( 2 x ) = y
x ∗ l o g 1 0 ( 2 ) = y
Plugging 6561 in for x gets you the answer, 1975 .