Question

6^n+9^n/6^n+4^n=64/729 then n=?​

Answer 1

Answer:

45930192528412568833367434565

Answer 2

Question:

$\dfrac{6^n + 9^n}{6^n + 4^n } = \dfrac{64}{729}$

Take out common factor:

$\dfrac{3^n(2^n + 3^n)}{2^n(3^n + 2^n) } = \dfrac{64}{729}$

Cancel off common factor:

$\dfrac{3^n}{2^n } = \dfrac{64}{729}$

Write the right-hand-side as a exponent:

$(\dfrac{3}{2 } )^n = \dfrac{64}{729}$

$(\dfrac{3}{2 } )^n = (\dfrac{2}{3}) ^3$

Therefore:

$n = 3$

Answer: n = 3