SOLUTION: Please help. I don't understand how to solve these Let r = log(7)17, s = log(5)17, t = log(7)5 Write the following expressions in terms of r, s, and/or t. The change of base

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help. I don't understand how to solve these Let r = log(7)17, s = log(5)17, t = log(7)5 Write the following expressions in terms of r, s, and/or t. The change of base      Log On


   

Question 933032: Please help. I don't understand how to solve these
Let r = log(7)17, s = log(5)17, t = log(7)5
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. Your answer for all but the second one should use just one letter.
log(base7) 5th root sqrt(17) =
log(base7)85 =
log(base17)7 =
log(base25)17=
log(base5)(17(7^(log(base49)5) =
THANKS
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = log(7)17, s = log(5)17, t = log(7)5
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. Your answer for all but the second one should use just one letter.
log(base7) 5th root sqrt(17) =%281%2F10%29log%287%2C%2817%29%29=r%2F10
log(base7)85 =log%287%2C%2817%29%29%2Blog%287%2C%285%29%29=r%2Bt
log(base17)7 =log%287%2C%287%29%29%2Flog%287%2C%2817%29%29=1%2Fr
log(base25)17=log%285%2C%2817%29%29%2Flog%285%2C%2825%29%29=t%2F2
log(base5)(17(7^(log(base49)5)
(log(base49)5)=log%287%2C%285%29%29%2Flog%287%2C%2849%29%29=t%2F2
(7^(log(base49)5)=7^(t/2)
=log%287%2C%2817%29%29%2Flog%287%2C%285%29%29%2B%28t%2F2%29log%287%2C%287%29%29=r%2Ft%2Bt%2F2 (had to use 2 letters)