SOLUTION: If A=log 2 and B=log 3, write the following in terms of A and B: a)log 36 b)log 54 c)log (8 sqrt 3) d)log (20.25) e) log (0.8)

Algebra ->  Exponents -> SOLUTION: If A=log 2 and B=log 3, write the following in terms of A and B: a)log 36 b)log 54 c)log (8 sqrt 3) d)log (20.25) e) log (0.8)      Log On


   

Question 701467: If A=log 2 and B=log 3, write the following in terms of A and B:
a)log 36
b)log 54
c)log (8 sqrt 3)
d)log (20.25)
e) log (0.8)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If A=log 2 and B=log 3, write the following in terms of A and B:
a)log 36 = log(3^2*2^2) = 2log(3)+2log(2) = 2(B + A)
b)log 54 = log(27*2) = log(3^3)+log(2) = 3log(3) + log(2) = 3B + A
c)log (8 sqrt 3) = log(2^3*3^(1/2)) = 3log(2) + (1/2)log(3) = 3A + (1/2)B
d)log (20.25) = log(81/4) = log(81)-log(4) = 4log(3)-2log(2) = 4B-2A
e) log (0.8) = log(8/10) = log(8)-log(10) = 3log(2)-1 = 3A-1
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Cheers,
Stan H.
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