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Question
Express the following as a single logarithm:
`2 + 1/2 "log" 9 - 2 "log" 5`
Sum
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Solution
`2 + 1/2 "log" 9 - 2 "log" 5`
= `2 + 1/2 "log" 3^2 - 2 "log" 5`
= `2 "log" 10 + 1/2 xx 2 "log" 3 - 2 "log" 5`
= log 102 + log 3 - log 52
= log 100 + log 3 - log 25
= `"log" (100 xx 3)/(25)`
= log 12.
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Expansion of Expressions with the Help of Laws of Logarithm
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