Question

3 rase to the power n minus 3 raise to the power n-2 is equal to 648 . Find n raise to the power 3

Answer 1

Question:

3^n - 3^(n - 2) = 648

Find n^3.

Solution:

3^n - 3^(n - 2) = 648

=> 3^(n - 2 + 2) - 3^(n - 2) = 648

=> 3^(n - 2) · 3^2 - 3^(n - 2) = 648

=> 3^(n - 2) (3^2 - 1) = 648

=> 3^(n - 2) (9 - 1) = 648

=> 3^(n - 2) · 8 = 648

=> 3^(n - 2) = 648 / 8

=> 3^(n - 2) = 81

Now,

log_3 (81) = n - 2

=> log_3 (3^4) = n - 2

=> 4 log_3 (3) = n - 2

=> 4 · 1 = n - 2 [Because log_a (a) = 1]

=> 4 = n - 2

=> n = 4 + 2

=> n = 6

So,

n^3 = 6^3 = 216