the book simply says find the exact value of each expression. without a calculator. using properties of logarithms.( which it lists, but I can't see where they apply)
1. log6^18-log6^3
for this I just divided 18 by 3 getting 6. log6^6=1? is that right?
2.log3^8 * log8^9
for this i tried change of base. I did
(logb^8/logb^3) * (logb^9/logb^8)
3. e^(log(e^2)^16)
I'm completely lost on this one. Supposedly these are all really easy to do without a calculator. i just don't know how to do them. Any help would be greatly appreciated.
1. Correct.
2. Change of base is the right way to go here but you pick a given value of b: usually base e or base 10:
3. Do you mean?
-> the base of the log is e^2
it's an unusual base so I'd use the change of base as above ignoring the base of the exponent for now (the e at the start). I am choosing base e because then it will cancel at the end.
Bringing in our exponent we get
Properties:
Logarithmic identity