Question

simplify the following: write in terms of a & b w/o logs or powers, where

log2(3)=a
log3(5)= b

1. log 2(3/2)
2. log3(45)
3. log2(1/9)
4. log16(3)
5. log4(27)

I'm pretty sure I know how to do 1 and 3
1. log2(3/2)= a-1
3. log2(1/9)= -a^2

The rest i'm unsure...

Answer 1

2) log3(45) = log3(9x5) = log3(3^3) + log3(5) = 3log3(3) + b = b+3

Answer 2

4) let log16(3) = y
you have => 3 = 16^y or 3 = 2^(4y)
=> log2(3)=4y
or y = 1/4*a

you can do the other in similar way

Answer 3

the first answer is actually wrong because 3^3 = 27 so it's actually log3(3^2) + log3(5) => logb(b^x)=x so 2+b