中四數學比較大小

a = 600^4500
==> log a = 4500 log 600 = 12501.68063b = 2400^3600
==> log b = 3600 log 2400 = 12168.76047c = 3600^2400
==> log c = 2400 log 3600 = 8535.126002d = 4500^600==> log d = 600 log 4500 =2191.927508As log a > log b > log c > log dTherefore, a > b > c > dThat is, 600^4500 has the greatest value.

The operation of base and index are not the same, my friend.

Compare 4^6 and 6^4 is not the same as compare 2^3 and 3^2

4^6 > 6^4 but 2^3 < 3^2

whichof the follow has greatest value?
a. 600^4500
b.2400^3600
c.3600^2400
d.4500^600
Sol
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比較 2^15，8^12，12^8，15^2
8^12/12^8=2^36/(2^16*3^8)=2^20/3^8>1
So
8^12>12^8>2^15>15^2
2400^12>3600^8>600^15>4500^2
2400^3600>3600^2400>600^4500>4500^600
b>c>a>d