You have to know the special rules of logarithms:
Using the facts that log2 = 0.3010 and log3 = 0.4771, find the values of the following
a) log6
1. You must observe that 6 is 2·3
2. You must know the rule of logarithms that states
log(U·V) = log(U) + log(V)
Let U = 2 and V = 3 and substitute:
log(2·3) = log(2) + log(3) = 0.3010 + 0.4771 = 0.7781
b) log1.5
1. You must observe that 1.5 is which is
2. You must know the rule of logarithms that states
log() = log(U) - log(V)
Let U = 3 and V = 2 and substitute:
log() = log(3) - log(2) = 0.4771 - 0.3010 = 0.1761
c) log1/2
1. You must observe that is 2-1
2. You must know the rule of logarithms that states
log(UV) = V·log(U)
Let U = 2 and V = -1 and substitute:
log() = log(2-1) = -1·log(2) = -1·0.3010 = -0.3010.
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Note: You can do log() another way, like (b):
Use the rule of logarithms that states
log() = log(U) - log(V)
Let U = 1 and V = 2 and substitute:
log() = log(1) - log(2)
You must know that log(1) = 0,
[Since 10 must be raised to the 0 power to get 1]
Then
log() = log(1) - log(2) = 0 - 0.3010 = -0.3010
Edwin