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46.

A rough estimate can be arrived at if you consider the fact that 210 = 1024 which is approx 103.

Then 2150 = (210)15 ≈ (103)15 = 1045 which is a 46 digit number.

A more precise answer can be obtained by using logarithms.

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14y ago
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Q: How many digits are there in 2 raise to 150?
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