SOLUTION: Why is log[base9]x equivalent to log[base27]x/log[base27]9? How would you prove it algebraically? Thank you!

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Question 861718: Why is log[base9]x equivalent to log[base27]x/log[base27]9? How would you prove it algebraically?
Thank you!
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
log%289%2Cx%29=log%2827%2Cx%29%2Flog%2827%2C9%29

What happens if the Change Of Base Formula is used for the left member? Its derivation (Change Of Base) is a separate but important process.

Following the change of base formula to log%289%2Cx%29 gives log%2827%2Cx%29%2Flog%2827%2C9%29. What you are then wanting to know is, how to derive the Change Of Base Formula?
You may look at and hopefully understand the proof found in http://en.wikipedia.org/wiki/Logarithmic_identities#Changing_the_base. Look at the sections, "changing the base", and "proof".