Remember the basic fact: y = a^x <==> loga y = x

translate to "how many times of multiplication of a" can get you y?

for example, log264 = 6

logx(1/8) = 3,

then x = ?

x^3 = 1/8, so x = 1/2

log (1/16) x = -0.75,

then x = ?

(1/16)^(-3/4)

= [(1/2)^4]^(-3/4) note: (a^n)^m = a^(n*m)

= (1/2)^(-3)

= 1/[(1/2)^(3)] note: reciprocal for negative exponent

= 1/(1/8)

= 8

Review p.141 yellow book, see the graph, feel the grow of log function.

logaXY = logaX + logaY

loga(X/Y) = logaX - logaY

logaX^n = n logaX

loga^nX = (1/n)logaX

a^(logaX) = X

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