Question 749672
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You have to know the special rules of logarithms:
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Using the facts that log2 = 0.3010 and log3 = 0.4771, find the values of the following
a) log6
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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
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b) log1.5
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1. You must observe that 1.5 is {{{1&1/2}}} which is {{{3/2}}}

2. You must know the rule of logarithms that states 

log({{{U/V}}}) = log(U) - log(V)

Let U = 3 and V = 2 and substitute:

log({{{3/2}}}) = log(3) - log(2) = 0.4771 - 0.3010 = 0.1761
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c) log1/2
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1. You must observe that {{{1/2}}} is 2<sup>-1</sup>

2. You must know the rule of logarithms that states 

log(U<sup>V</sup>) = V·log(U) 

Let U = 2 and V = -1 and substitute:

log({{{1/2}}}) = log(2<sup>-1</sup>) = -1·log(2) = -1·0.3010 = -0.3010.

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Note:  You can do log({{{1/2}}}) another way, like (b):

Use the rule of logarithms that states 

log({{{U/V}}}) = log(U) - log(V)

Let U = 1 and V = 2 and substitute:

log({{{1/2}}}) = 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({{{1/2}}}) = log(1) - log(2) = 0 - 0.3010 = -0.3010

Edwin</pre>