Tuesday 19 February 2013

Lesson Summary 19/2/2013: Wee Chang Han

Logarithm 

Laws of Logarithm:

1.
a^x = y
is equals to:
log a(y) = x

2. 
log10 = lg
log e = l(n), n = natural log.

3.
lg 1 = 0
log10 (1) = 0
10^0 = 1
Because:
loga(1) = 0
a ^0 = 1
where a ≠0.

4.
loga(a) = 1
where a ≠ 0, a >0
log10(10) = 1
because:
log10(10) = 1
10^1 = 10

Note:


5.
log10(-5) = error?
why?

-5 = 10^?

there is no value for the power of 10 to become -5, therefore log a base b = c, where a ≠ a negative integer or  < 0.

6.
loga(b) = log10(b) / log10(a)
            = ln(b) / ln(a)
            
caution!:
lg(b)/lg(a) ≠ b/a (do not cancel!!)

Correct:
lg(b)/ lg(a) = calculate both the top and the bottom.

7.
logc(ab) = logc(a) + logc(b)

8.
logc (a/b) = logc (a) - logc (b)

9.
log10(100) = log10(10)^2
                  = 2log10(10)
                  = 2

note:
loga(b)^n = n loga(b)


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