If you have the equation y kxn and you take the log of both

If you have the equation, y = kxⁿ and you take the log of both sides to get log y = 0.5 log(x) + 2.

a) What is the value of n?

b) What is the value of k?

Solution

y = kxⁿ

take the log of both sides

log y = log kxⁿ

[since log(ab)=log(a)+log(b)]

log y = log k +logxⁿ

[since log(a^b)=blog(a)]

log y = log k +logxⁿ

log y = log k +nlogx

log y =nlogx +log k

comparing with

log y = 0.5 log(x) + 2

n=0.5

log k =2

[since log a =b => a=10^b]

k =10²

k =100

a) value of n=0.5

b) value of k =100