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Logarithms
Laws of logarithms
For a,b,c,x,y>0, a≠1 and r is a real number
1. Loga (a) =1
2.Loga (1) =0
3.Loga (x^r)=r loga (x)
4.Loga (xy) = loga (x) +loga (y)
5. Loga (x/y)= loga (x) — loga (y)
6. Change of base; loga (b) = logc (b)/logc (a)

Index to logarithm form

Y=a^x  —> loga (y) =x

Log10 = lg
Loge =ln

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base to base
logaY = X
Y = A^x

laws
1. logaX^r = rlogaX               (power law)
2. logaXY = logaX + logaY  (product law)
3.loga(X/Y)+logaX - logaY  (quotient law)
4. logaB= logcB/logcA        (change of base law)
5. logaM = logaN, N=M

special cases
logaA = 1
loga1 = 0

graphs
asymptote; the line the graph approaches but never touches
to find asymptote:
lg(x + a)
(x + a) = 0