If y = x ^ n (or y = x 'to the power n'), I know x and y how do I find n?

Question

Specific example:

1/6 = (3/4)^n

I'm sure I remember a relatively simple equation!

HELP!

Answer 1

n = log(y) / log(x)

or in your example about 6.23

Answer 2

1/6 = (3/4)^n
taking log both side
log 1 -log 6 =n(log 0.75)
0- 0.77815125 = n(-0.124938736)
n=0.77815125/0.12938736
n=6.228262519

Answer 3

use logarithmic
1/6 =(3/4)^n
6^ -1 = (3/4)^n
log 6^ -1 = log (3/4)^n
-1 log 6 = n log (3/4)
n= (-1 log6)/(log (3/4))
n=6.22826

Answer 4

Apply the law of logarithms.

Since y=x^n, take the log of both sides...

log y=log x^n

Apply the Power Law which is done by removing the exponent and multiplying it to the log which is belongs (log a^b=b log a)

log y= n log x

Isolating n, we get:

n=(log y)/(log x)

or log of y to the base x using change of base formula.

Cheers.

Answer 5

y = x^n

take logs of both sides (in this case i am choosing logs to base e)

lg y = (lg x)*n >>>>> n = (lg y)/(lg x)

use a calculator and the prob is solved in secs

in your example n=(lg(1/6)/lg(3/4)) =6.228262519

Answer 6

y = x^n
lgy = lgx^n
lgy = nlgx
n = lgy/lgx

So,
1/6 = (3/4)^n
lg(1/6) = lg(3/4)^n
lg(1/6) = nlg(3/4)
n = lg(1/6)/lg(3/4)
n = 6.23 (correct ot 3 sig fig)

Answer 7

y = x^n

then Log y = logx times n

log y/log x = n

Answer 8

Note, you can use 'log' or 'ln' on your calculator for this.