Given that 3 to the power of - n = 0.2 find the value of (3 to the power of 4) to the power of n.

so 3^-n=0.2 find value of (3^4) ^n my working out: 1) 3=n surd 0.2 2) n must be decimal number 3) cuberoot o. 2=0.5848035476425733 4) so n=0.5848035476425733 5) (3^4) ^0.5848035476425733=13.0643801669 6) so that answer is the value of (3^4) ^n

Question

Mathematics

Ramos

30 August, 11:56

Given that 3 to the power of - n = 0.2 find the value of (3 to the power of 4) to the power of n.

so 3^-n=0.2 find value of (3^4) ^n my working out: 1) 3=n surd 0.2 2) n must be decimal number 3) cuberoot o. 2=0.5848035476425733 4) so n=0.5848035476425733 5) (3^4) ^0.5848035476425733=13.0643801669 6) so that answer is the value of (3^4) ^n

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Answers (1)

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Bernard Nielsen · Answer 1

3^-n = 0.2

1 / 3^n = 0.2

1 / 0.2 = 3^n

5 = 3^n

Log 5 = log (3^n)

Log 5 = n log 3

N = log 5 / log 3

N = 1.4650

So (3^4) ^n = (3^4) ^1.4650 = 625