Question

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

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