Find: a) log12(1/144) b) log81(3) c) log32(1/2) but without a calculator!!?
a) log12(1/144) b) log81(3) c) log32(1/2)
12, 81, and 32 ARE ALL SUBSCRIPTS (the base for each log).
So the answer is suppose to be a) -2, b) (1/4), c) -(1/5).
What I need to know is how to get to those answers WITHOUT the aid of a calculator. I'm assuming, lets say for part a) you are suppose to change it to 12^x= 1/144... but how can I figure out x if this is the right method?
Atualizada:Brenda:
How were you able to figure out that if 12^x=1/144, then x= -2? (and for part b and c).
Remember, I need to know how to do this WITHOUT a calculator... So I need you to explain the steps for me in detail as to how you figured that out. Thanks!!
Answers & Comments
Verified answer
x is the number you are trying to find
so
log 12 (1/144) = x
12 is your base x is your exponent and 1/144 is the answer you get when you write it out
12 ^ x = 1/144
12^ x = 12^-2 (because 12^2 is 144 and the negative makes it the reciprocal. So 4^-2 would be 1/16)
Since bases are the same....
x = -2
2. log 81 (3) = x
81^x= 3
(3^4)^x = 3^1 because 3*3*3*3=81 and anything to the first power is itself
3^4x = 3^1 law of exponents
bases are the same
4x = 1
x=1/4
3. log 32 (1/2) = x
32^x = 1/2
(2^5)^x = 2^-1
2^5x = 2^-1
5x= -1
x=-1/5
a.
log(base12) (1/144)
12^x = 1/144
x = -2
b.
log(base81) (3)
81^x = 3
1/4
c.
log(base32) (1/2)
32^x = 1/2
x = -1/5