The relationship between ln (10) and log (e)

I know they're reciprocals because it said so in the book, but can anyone explain why??

Please provide mathematical proof... Thanks in advance ;)

http://www.flickr.com/photos/dwread/6479…

ln(10)=log(10)/log(e)=1/log(e)
log(e)=ln(e)/ln(10)=1/ln(10)