# EVALUATING LOGARITHMS (using LOG Properties) x = a

```EVALUATING LOGARITHMS
(using LOG Properties)
EXPONENTIAL FORM
LOGARITHMIC FORM
x = ay
logax = y
NOTE:
Example 
If no base is given, a base of 10 is understood. Ex. log7 = log107
Calculators are programmed in base 10. Ex. log7 = 0.845098
Calculate, rounding to 1 decimal place where required:
a)
log100
b)
log500
Properties of Logarithms:

log a 1  0
ex. log 5 1 

log a a x  x
ex. log 6 6 2 

a
Example 
log a x
x
ex. 8log 8 64 
Evaluate each of the following expressions without a calculator:
a)
log 7 1
b)
5
log5 25
c)
 1 
log 

 100 
d)
log 5 125
e)
log 2 (4)
f)
log 6 36  log 5 25
Example 
Solve for x in each of the following:
a)
log x 64  6
b)
log 3 x  2
Example 
Estimate the value of log420 using a “guess &amp; check” method.
Example 
A sample of the radioactive substance X13 with mass P grams, is
determined by the given equation where t is the time in years and
h is the half-life of the substance. If the half-life of X13 is 4 years
and the initial mass of the sample is 1600g, determine how long it
will take for the substance to decay to a mass of 100g.
t
 1 h
M(t)  P 
2
Homework: p.466–467 #3–6, 8–12
```