(4/5)^3÷(-4/5)^3=(-1)^(3n) find the value of n
Answers
9^n * 3 ^2 * 3^n - 27^n /(3^(15) * 2^3) = 1/22
simplifying every exponential possible to power of 3
=> 3^(2n) * 3 ^2 * 3^n - 3^(3n) /(3^(15) * 2^3) = 1/22
adding up all possible powers of 3
=>3^(3n + 2) - 3^(3n) /(3^15 * 2^3) = 1/22
multiplying 8 both sides to remove 2^3 from denominator of second term in L.H.S.
=> 8 * 3^(3n + 2) - 3^3(n - 5) = 8/22
Taking common 3^3n on L.H.S.
=>3^3n * [ (8x9) - ( 3^-5)] = 8/22
Assuming 72 >> 3^-5
=>3 ^ 3n = 8 / (22 * 9 * 8)
Cancelling 8 from numerator and denominator
=>3 ^ 3n = 1 / (22 * 9)
Taking log base 3 on both sides
=> 3n = log ( 1/ (22 * 9) ) / log (3)
Finding the approximate value of R.H.S. using logarithmic knowledge (or calculator :P)
=> 3n = -4.8136
Dividing 3 on both sides we get :
n = -1.6 (approx.)