Math, Feeling The Logarithm (Concents)

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