Question

If Log"2n"(1944) = Log"n" (486√2), determine the value of n^6.
does anyone no how to do this?

Answer 1

the "2n" and "n" are subscripts of log

Answer 2

let Log"2n"(1944) = x
then (2n)^x = 1944
also Log"n" (486√2) = x
and n ^x = 486√2

(2n)^x / n ^x = 1944 / 486√2
2^x = 2.828427125
x ln 2 = ln 2.828427125
x = 1.5

Answer 3

plug x=1.5 into n ^x = 486√2
n ^ 1.5 = 486√2
1.5 ln n = ln 486√2
n = 77.88148
n^6 = 2.2315 * 10^11

not sure if this is right ?- such a big number.

Answer 4

i cant see any mistake after reviewing it again romoor though there might be another easier way of doing it

Answer 5

lets see if the value of x and n satisfy the first log:
(2 * 77.88148)^1.5 = 1944 - yes that's ok