# solving for an exponent

• Mar 19th 2009, 05:26 PM
wonder-wookie
solving for an exponent
I'm having trouble with a simple math problem that I embarrassingly should know how to solve.

X^n = n^10

X is a constant value.
Solve for n.

Can anyone point me in the right direction?

Thanks!
• Mar 19th 2009, 05:49 PM
mr fantastic
Quote:

Originally Posted by wonder-wookie
I'm having trouble with a simple math problem that I embarrassingly should know how to solve.

X^n = n^10

X is a constant value.
Solve for n.

Can anyone point me in the right direction?

Thanks!

Take the log of both sides (it doesn't matter which base you use, base 10 is convenient). Now use a well known log rule to get a linear equation in n. Solve this equation.
• Mar 19th 2009, 07:03 PM
wonder-wookie
ok, lets see if I have this correct...

log(X^n) = log(n^10)
n log (X) = 10 log (n)

n 10
----- = ------
log (n) log (X)
That is as far as I got. How can I simplify the left hand side so there is a single N term?
• Mar 19th 2009, 09:07 PM
mr fantastic
Quote:

Originally Posted by wonder-wookie
ok, lets see if I have this correct...

log(X^n) = log(n^10)
n log (X) = 10 log (n)

n 10
----- = ------
log (n) log (X)
That is as far as I got. How can I simplify the left hand side so there is a single N term?