Question

find the value of n if

$({ \frac{3}{4} })^{n - 1} { \times( \frac{16}{9}) }^{1 - n} = \frac{27}{64}$
​

Answer 1

Ratio is given so we can write it as following

4!(n−4)!

n!

2!(n−2)!

n!

=

1

2

2!(n−2)!

n!

×

n!

4!(n−4)!

=

1

2

(n−2)(n−3)(n−4)!

1

×

1

4×3×(n−4)!

=

1

2

2n

2

−10n+12−12=0

2(n

2

−5)=0

n=±

5