Question
If log 27 = 1.431, then the value of log 9 is:
Answer: Option C
$$\eqalign{
& \log 27 = 1.431 \cr
& \Rightarrow \log \left( {{3^3}} \right) = 1.431 \cr
& \Rightarrow 3\,\log \,3 = 1.431 \cr
& \Rightarrow \log \,3 = 0.477 \cr
& \therefore \log \,9 = \log \left( {{3^2}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\,\log \,3 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {2 \times 0.477} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.954 \cr} $$
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$$\eqalign{
& \log 27 = 1.431 \cr
& \Rightarrow \log \left( {{3^3}} \right) = 1.431 \cr
& \Rightarrow 3\,\log \,3 = 1.431 \cr
& \Rightarrow \log \,3 = 0.477 \cr
& \therefore \log \,9 = \log \left( {{3^2}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\,\log \,3 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {2 \times 0.477} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.954 \cr} $$
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