Question

I don't understand how to do these w/o calc.
I tried to write it in a way that will make someone understand how to read it. Hope I typed it clear enough.Thanks so much for the help anyone!
How to find the exact value of logarithm:

10. log5^100 -log5^4

11. log4^8 +log4^8

12. log squareroot 100
13. log4^40 -log4^10

19. log 3^20.25 +log3^4

22. 7 log2 ^16 +log2 (1/16)
27. log 2 +log 5-log 10

31. 2 ln e^6 -ln e^5

36. log 100 + log 10,000

Answer 1

log5 (25)

5^(log5(25) = 25
but
5^2 = 25
so
log5(25) = 2

Answer 2

you must memorize the 3 main rules of logs

1. log (AB) = log A + log B
2. log (A/B) = logA - logB
3 log (A^n) = nlogA
for any base of the log as long as the base is the same throughout the equation

e.g.
#22
7log 2^16 + log (2^(1/16)) , I assumed a typo here
= 7(16)log 2 + (1/16)log 2
= (1793/16) log 2

#11
log 4^8 + log4^8
= log (4^8 * 4^8)
= log 4^16
or
= 16 log4