Question

Which is bigger 2 ^845 or 5 ^362?

Answer 1

2^845 is greater than 5^362.

Explanation:

To compare the two numbers, we can evaluate them using the logarithm function with base 2 and base 5 respectively.

2^845 = 2^(845 * log2(2)) = 2^(845 * 1) = 2^845

5^362 = 5^(362 * log5(5)) = 5^(362 * 1) = 5^362

The logarithm of a number is the exponent to which the base must be raised to give that number. Since logarithm function is a monotonically increasing function, if we compare log base a of x to log base a of y, logarithm of x is greater than y if x is greater than y.

So 2^845 > 5^362 if 845 > 362 * log5(2)

We can calculate log5(2) = log5(2)/log5(2) = 0.6309

so 845 > 362 * 0.6309

845 > 229.8198

so 845 is greater than 229.8198, therefore 2^845 is greater than 5^362.

Answer 2

Explanation:

2^845 = 2^5(2^7)^120 = 32(128)^120,

5^362 = 5^2(5^3)^120 = 25(125)^120,

2^845 is bigger.