log base 2n 1944 = log base n (486* (2)^1/2)

Question

find n^6

Answer 1

Let logbase2n 1944 = x

(2n)^x = 2^x * n^x = 1944

n^x = 486*2^1/2

2^x * 486*2^1/2 = 1944
2^x = 4*2^-1/2 = 2^3/2
Therefore x = 3/2

logbase2n 1944 = 3/2

(2n)^3/2 = 1944
Take the 2/3 power of both sides
2n = 155.76
n = 77.88

n^6 will be quite large.

See if you agree. I may have goofed somewhere

Answer 2

sounds quite right to me. thanks!