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andriy [413]
3 years ago
12

Compare the numbers 26^39 and 39^26. Which one is bigger? Are they the same? No calculators.

Mathematics
1 answer:
nydimaria [60]3 years ago
7 0

Answer:

26^{39} is greater.

Step-by-step explanation:

Given numbers,

26^{39}\text{ and }39^{26}

∵ HCF ( 26, 39 ) = 13,

That is, we need to make both numbers with the exponent 13.

26^{39}=((13\times 2)^3)^{13}=(13^3\times 2^3)^{13}=(13^3\times 8)^{13}=(13^2\times 104)^{13}

(\because (a)^{mn}=(a^m)^n\text{ and }(ab)^m=a^m.a^n)

39^{26}=((13\times 3)^2)^{13}=(13^2\times 3^2)^{13}=(13^2\times 9)^{13}

Since,

13^2\times 104>13^2\times 9

\implies (13^2\times 104)^{13} > (13^2\times 9)^{13}

\implies 26^{39} > 39^{26}

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