SOLUTION: Convert the fallowing expression a^(1/ln a) using base e, for a > 0 and a≠1. So i know how to convert the simple equations but im having difficulty converting like this one

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Convert the fallowing expression a^(1/ln a) using base e, for a > 0 and a≠1. So i know how to convert the simple equations but im having difficulty converting like this one       Log On


   

Question 896086: Convert the fallowing expression a^(1/ln a) using base e, for a > 0 and a≠1. So i know how to convert the simple equations but im having difficulty converting like this one
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%282%2C1%2C%22%22%2Ca%5E%281%2Fln%28a%29%29%29

Let x equal to the expression:

matrix%282%2C1%2C%22%22%2Cx%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2Ca%5E%281%2Fln%28a%29%29%29

Take natural logarithms of both sides:

matrix%282%2C1%2C%22%22%2Cln%28x%29%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2Cln%28a%5E%281%2Fln%28a%29%29%29%29

Use the rule of logarithms ln%28P%5EQ%29=Q%2Aln%28P%29

ln%28x%29%22%22=%22%22%281%2Fln%28a%29%29ln%28a%29

ln%28x%29%22%22=%22%22%281%2Fcross%28ln%28a%29%29%5B1%5D%29cross%28ln%28a%29%29%5E1

ln%28x%29%22%22=%22%221

Use the fact that the natural log equation ln%28P%29=Q 
is equivalent to the exponential equation e%5EQ=P

e%5E1%22%22=%22%22x

e%22%22=%22%22x

Answer: it simplifies to e.

Edwin