Exact Value of 6561(1/ln(9)) Using Logarithmic Form

[imull]

Homework Statement

Find the exact value of the expression: 6561^(1/ln(9))

Homework Equations

log_ax=(1/ln(a))(ln(x))

The Attempt at a Solution

I thought that I would start it by putting the expression into logarithmic form: log₆₅₆₁x=1/(ln(9)). I am not sure where to go from here though.

 

[D H]

Try a different base.

 

[imull]

Such as?

 

[Dick]

Such as?

You already have an exact value. It's just what's printed there. You can express it in other ways that don't look terribly much simpler. I suspect that the log in the exponent might be intended to be a different base. Is that the exact problem? Try factoring 6561 to see why I might think so.

 

[D H]

You already have an exact value. It's just what's printed there.

Exactly.

You can express it in other ways that don't look terribly much simpler.

It can be expressed in a much more compact form than 6561^{(1/ln 9)}.

Try factoring 6561 to see why I might think so.

That's a very good suggestion.

 

[imull]

Thank you both very much. I'll work on it.