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)