How Can You Simplify Logarithmic Expressions Using the Change of Base Formula?

[coolkid800]

this is what I'm having trouble with:

Let r = log6 17, s = log4 17, t = log6 4.

Write the following expressions in terms of r, s, and/or t. The change of base formula may be helpful in finding some of these logarithms.

log16 17 =

http://www.webassign.net/www31/symImages/6/a/1835a244d7715d29ef2d1f41e45aff.gif

log16 17(6^(log36 4) =

http://www.webassign.net/www31/symImages/d/4/9b6ebc66e4a9ccb204874138ac34c3.gif

Plz help!

 

[cristo]

Well, you've been given a hint. What are the "change of base" formulae?

 

[coolkid800]

lol I don't know, I tried looking in my textbook and I couldn't find anything!

 

[Helical]

Change of base is explained here:
http://www.mathwords.com/c/change_of_base_formula.htm

 

[coolkid800]

i don't understand how i got the first one wrong, isn't it supposed to be r/2t

 

[Feldoh]

Change log_{16}17 to base 4.

 

[coolkid800]

okay the first one that i asked u guys, the answer is s/2

apparently i thought i got the last one right, but it was wrong, i put s(6^t/2)

but it was s+.5, anybody kno why?!?

 

[cristo]

Have you looked at the change of base formula provided in the link above? For the first question, follow the hint by Feldoh, and use the change of base formula; so, \log_{16} 17=\frac{\log_4 17}{\log_4 16}. Can you continue?

Incidentally, you should post in the homework forums in future.