SOLUTION: Using the facts that log2 = 0.3010 and log3 = 0.4771, find the values of the following a) log6 b) log1.5 c) log1/2 Can you please help me out? Thanks so much in advance Al

You have to know the special rules of logarithms:

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

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

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