if log(base 2n)1944 = log(base n)286root2, find the values of n^3

Answer 1

if log(base 2n)1944 = log(base n)286root2, find the values of n^3

first focus on the left side and use change of base rule:

 log(base 2n)1944 = log(base n)1944/ log(base n)2n

cancel the denominator by multiplying it to both sides

log(base n)1944 = (log(base n)2n)* log(base n)286root2

log_n1944 = log_n2n*log_n286Ö2

log_n2n*log_n286Ö2 = log2n*log286Ö2/(logn)^2

cancel the denominator by multiplying it to both sides

log2n*log286Ö2 = 2*logn* log_n1944 =2* log1944

log2n* 2.6 = 2*3.28869626059 = 6.57739252118

log2n* 2.60688103096 = 6.57739252118

log2 + logn = 2.523088873

0.3010299957 +logn = 2.523088873

Log₁₀n = 2.222058877

 

n = 10^2.222058877

use your calculator and find n^3

this is an interesting question, hope that helps